Cannibal prevention (if you can afford the ammo):

Savage rifles tend to be way overpriced. They do have a few winners out there, and a few losers, speaking from experience.
338 Lapua is great for the long range sniping of apocalyptoids, but likely we will encounter them at far closer distances.
308 WIN just as good for longer distances. Cheaper ammo too.
As with everything, such as daily prayer, you have to practice frequently with whatever thou hast.  
With the moral question about the gang of men chasing a woman with or without child, I doubt they will want to have a high tea social. ;)In such a situation, you are defending the weak and helpless.Also calls up the need for a semi auto rifle. Lots of 5.56 mm and 7.62 x 39 surplus out there, even in Canada eh!

1) FCP110 is $1,300 +/-.  All other weapons chambered in same caliber from ANY other mfg tend to be 2-3x higher (unless there is something out there I don't know about, which is not likely);

2) Agree: I would not pick this weapon for shots closer than 300 yards (but you wouldn't purchase it as a close quarter battle rifle);

3) .308 WIN cannot even come close to .338 in ELR shooting.  .338 currently holds world record verified kill in Afghanistan at 2,708 yards.  Navy seals don't use .308 WIN for anything longer than 500 yards, if they can help it.

If you were referring to .308 Win Mag or .308 short mag, those reach out a bit longer, but probably top out around 1,000 yards.

3) .308 WIN cannot even come close to .338 in ELR shooting.  .338 currently holds world record verified kill in Afghanistan at 2,708 yards.  Navy seals don't use .308 WIN for anything longer than 500 yards, if they can help it.

You're picking on my go to cartridge.
Here's an amusing video for those who think that the .308 is inadequate. 

After the worldwide cataclysm, which brought about TEOTWAKI ("the end of the world as we know it"), instituting a world WROL ("without rule of law"), Catholic survivors will have a whole new set of moral problems to deal with.

Certain types of cataclysm will make the production of food almost impossible for a time (e.g., nuclear war: Polluted ground, radioactive meat, nuclear winter blocking sunlight), and in these types of disasters, cannibalism will emerge as the primary threat: People will hunt people for food.

Here is a moral scenario I wondered about:

Hidden in a field above my bunker, I spot a woman and child being pursued by a gang of men who, if they capture them (which seems imminent), will rape, murder, and eat them.  

It seems there are a number of (apparent) conflicting moral principles which would lay claims upon my duties and reaction:

1) Necessity imposes a grave obligation to come to the physical aid for anyone who has the possibility of rendering it (i.e., I may sin gravely if I do nothing, and be damned);

2) Duty of state: If I attempt to intervene, I will be overwhelmed, killed, and my family will be without protection, and in turn probably suffer the same fate as the woman and child.

Questions:

1) Is it the probability of victory which determines whether or not the duty to intervene compele one?

2) Or, will I be damned for intervening, knowing I will probably betray my family to the same fate if I intervene?

What would be the Catholic thing to do?

As an aside, this difficult situation and decision suggests Catholics group themselves into their own militias/prepper groups, and you will have less liklihood of having to wrestle with such situations (i.e., If we had a militia, we would surely intervene and wipe out the marauders).

Interesting question.

The Catholic thing to do would be to do what you can to help the innocent at the same time not getting killed yourself. But should you get killed, it would not have been in vain or for no good reason, so your own well being is secondary to trying to save the woman and child.

If the woman and child were your mother and sister and some other man in a bunker saw them fleeing the gang, what would you want that man to do - nothing or turn his back and just ignore the situation?

Then there's the Golden Rule; if you were the woman and child, wouldn't you want the man in the bunker to do something, anything? Futile though it may be, it might give you and child the chance to get away - even if it meant he got killed.

Perhaps it's easier to justify the above if you were to take the word "Catholic" out of the question, in which case it'd play out along these lines; "Sorry lady, you and the kid are on your own". Then you just go back in the bunker pitying them, close the door safe and sound, and get back to whittling spearheads.
 

Interesting question.

The Catholic thing to do would be to do what you can to help the innocent at the same time not getting killed yourself. But should you get killed, it would not have been in vain or for no good reason, so your own well being is secondary to trying to save the woman and child.

If the woman and child were your mother and sister and some other man in a bunker saw them fleeing the gang, what would you want that man to do - nothing or turn his back and just ignore the situation?

Then there's the Golden Rule; if you were the woman and child, wouldn't you want the man in the bunker to do something, anything? Futile though it may be, it might give you and child the chance to get away - even if it meant he got killed.

Perhaps it's easier to justify the above if you were to take the word "Catholic" out of the question, in which case it'd play out along these lines; "Sorry lady, you and the kid are on your own". Then you just go back in the bunker pitying them, close the door safe and sound, and get back to whittling spearheads.
 

Your whole post ignores the fact that the man debating about helping *has a wife a children back in the bunker*.
You said "so your own well being is secondary to trying to save the woman and child." You assume the man is single and unmarried, with no dependents either.

Why should that stranger woman and child have a higher claim on this man's life than his own wife and large family back in the bunker?

You even mock him, suggesting his day-to-day life isn't very noble, describing him whittling spearheads like some lonely bachelor or MGTOW, instead of having him hug his large number of children when he gets back.

Are we not our brother's keepers? - if so, then are we not bound to attempt to at least do *something*? Whether it be throw rocks at them from the bushes, ...

So you throw a rock at them just so you can pretend you're doing something?  In doing so, you reveal your position and expose your family to slaughter.  But, hey, you threw a rock.  If on the other hand you did happen to have "a machine gun", and therefore a good/reasonable chance of saving the person without jeopardizing your family, then of course you would intervene.

Here's where it gets very blurry.  I have a weapon and think I have about a 90% chance of success.  But if that 10% comes about, then I've just killed my family.  That's a real tough one.  I would think that your obligation to protect your family comes first.  You are the head of your family and are duty-bound to protect them moreso than you are to protect a stranger.  As Matthew said, this was a big part of the OP's scenario.  Now, if you're a loner, then absolutely I agree with you, that if you have ANY halfway realistic chance of saving the person, you would be duty bound to try ... even at risk of your own life.  But that is not OP's scenario.

You are the head of your family and are duty-bound to protect them moreso than you are to protect a stranger.  As Matthew said, this was a big part of the OP's scenario. 

I agree, family comes first.  As St Paul says, we are obligated to take care of our household first, then those of the "household of the Faith" second (i.e. Trad catholics).  Strangers would be "dead" last (pun intented).  ...I don't think you're obligated to put yourself in danger of death for most people (family excluded).  In such a situation, you'd have to rely on your gut instinct and a quick prayer.
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Another simpler scenario would be related to food.  Supposed you're on your way to the grocery to buy some very necessary things and you don't have much money to spare (i.e. think of an inflationary, food-ration situation).  On the way to the grocery (or after you bought the food) you come across a starving family.  I would give them a little of money or food I had, but I could not give them all, since my family's needs come first.  
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Certainly, God has worked many miracles in such situations for saints that gave away all the food they had, and they returned home to the house/monastery empty handed.  Yet, God miraculously provided them food later.  Surely God can work such miracles for us too, if we had Faith, but there's also prudence to think about.  I'm no saint, so I don't know if such circuмstances were meant to test the Faith of the house/monastery and if the actual saint was given the inspiration to give all he had to the strangers.  In absence of such an inspiration, I would think you help them out some, but not give them all.  Maybe my Faith is just lacking?  Maybe I'm just looking at this too materially?  It's very possible.  
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Though there was a story where the Cure of Ars gave away all the school's food and had the children pray all night for a miracle.  In the morning, the food prayed for was there, but St John Marie made the comment that he would never do such a thing again, because he didn't want to tempt Divine Providence.  St John worked many miracles but even he knew that there were limits.  Where does one draw the line between Faith in God and human prudence?  That's a difficult question.