CathInfo.com

He doesn't mean "anyone at all," period.  That sentence is part of a complete paragraph with a linear argumentation, so you have to read it in the sense of what came before.  He means "anyone at all" who is observing the natural law and its precepts.  Babies cannot "live honest lives," can they?  Again, babies are not at the age of reason so God cannot search their minds and hearts,  this passage does not apply to them.

That reading doesn't seem plausible at all; he doesn't say "... any such person," he says "anyone at all."  In any case, is your interpretation really that Pius IX would think that a good but unbaptized 12-year-old could go to heaven, because he has had some opportunities to "observe the natural law" and "live an honest life," while an unbaptized 4-year-old or newborn would surely be damned to Hell because he has not yet been afforded such an opportunity?  That's not a theory I've ever seen support for in traditional Catholic teachings.

Are you an adult convert?  If so, then you will know how you spent a long time searching, knowing that something was wrong with VII, but not knowing where to go.  In your heart you were -- probably -- Catholic at that time, before you found the true Church.  That is one example of how you can, theoretically, be in invincible ignorance.  God sees who WOULD embrace the truth if he were only able to find it.

Nope, cradle Catholic.  As to the conception you're putting forward here, it doesn't seem to have anything at all in common with the Traditional conception of Baptism of Desire, which was understood as applying to people like catechumens who were actively trying to join the Church but had to wait to be baptized.  If the type of directionless malaise and confusion you describe is sufficient for BoD, even among people who have never heard of the Church, then the doctrine is so fuzzy and ambiguous as to be nearly meaningless.