Two things.
First of all, if the missal were licit, even if the saying of it were not, it would then be certainly valid. Per Trent:
(Note: This canon, and the other canons of the Mass, refer to any Mass of the Church, not merely those of the Tridentine Rite, since otherwise it would still be permitted to say Masses in other rites preserved by Trent were invalid, heretical etc.)

Secondly, Trent does not forbid the saying of non-Tridentine Masses, so I don't see why it would be unlawful for priests to say a licitly promulgated Mass.

Two things.
First of all, if the missal were licit, even if the saying of it were not, it would then be certainly valid. Per Trent:

(Note: This canon, and the other canons of the Mass, refer to any Mass of the Church, not merely those of the Tridentine Rite, since otherwise it would still be permitted to say Masses in other rites preserved by Trent were invalid, heretical etc.)

Secondly, Trent does not forbid the saying of non-Tridentine Masses, so I don't see why it would be unlawful for priests to say a licitly promulgated Mass.

No, a missal is not the same thing as a Mass.  A missal is an inanimate OBJECT; a collection of rubrics.  A mass is a sacrificial ACT, performed by a PRIEST.  The former is a thing; the latter is an action.

No, this canon refers specifically to the Tridentine rite, as the whole purpose of the Council of Trent was to combat the heresies of Protestantism.  There existed, at the time of the late 1500s, only 1 rite of the mass, so Trent was explaining the importance and purpose of the Tridentine Mass, as opposed to Protestant heretics.

Correct, Trent does not forbid the saying of non-Tridentine masses.  But Quo Primum, which is an extension of Trent, specifically does....under penalty of a grave sin of disobedience.

A collection of rubrics... on the saying of a Mass. Saying that the Church can licitly issue missals and order them to be used, while also saying that the actual Mass itself is somehow illicit and not a Mass of the Church, is тαℓмυdist nonsense.

It did not and no there was not only one rite of Mass. Trent explicitly went out of its way to say it was preserving rites in use for more than 200 years at that time.

The underlined is your logical mistake.  There is no "order" than any catholic has to say/attend/accept/use/agree with/etc the new mass.  It is a completely optional liturgy.  There is no pain of sin and no loss of heaven for a catholic to ignore the new mass.  No church official has ever said otherwise.

Speaking of the Latin rite, yes, Quo Primum forbids all liturgies which aren't Tridentine.  The only exceptions are for rites 200+ yrs old at the time of 1571.

There's no such thing as "validly promulgated" because promulgate is a legal term, so a missal can only be LEGALLY promulgated.  The legality of an act is distinct from it's validity or morality.
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In this case, we are only dealing with legality.  Putting aside all Eastern/ancient rites, Quo Primum prevents the use of any non-Tridentine missal.  But (playing devil's advocate) QP does not prevent the CREATION of a new missal, only its use.

Well, to use a missal is to say a Mass.  You can't make a distinction between the 2.

From a legal standpoint, Quo Primum does not allow ANY missal to be used, except for it's own.  Just because a pope creates a new missal does not mean that it's ok to use.  Did St Peter create the Catholic Church?  Of course he didn't - Christ did.  Just because a pope creates a missal, doesn't mean it's part of the Faith.  He's not an oracle; he can't do whatever he wants.  That's ridiculous.

I don't know what you're saying here.  Different rites have different canons, but they essentially mean the same thing, because they are all from Apostolic origin.

Quo Primum's ban wouldn't apply to Paul 6's law?  You are correct and incorrect.
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1) As explained already, Paul 6's law does nothing more than create a new missal.  It does not say who has to use this missal, nor when, nor how, nor why, nor if there is a penalty for ignoring it.  So, according to law, all Paul 6 does is create a new missal.
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2) Paul 6 does not say that his new missal replaces Quo Primum; neither does he say that it is legally similar; nor does he say that it can be used, in spite of Quo Primum's restrictions.  In fact, Paul 6 does not address QP at all, except to reference it at the beginning when he is introducing his "new" rite.
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So, yes, each rite is legally on the same level...as far as "existence" is concerned.  As far as "using" the rite, no, the novus ordo is probably invalid, definitely illegal and definitely immoral.