@orthoformate (great name by the way!)
As I mentioned in my previous reply to you, this chemistry has been described in two papers by the great Al Padwa. The refs are: J. Org. Chem. 2006, 7391 and Org. Lett. 2006, 601.
Let me know if you don't have access to these journals but would like to look at these articles.
As to your argument that "Posts #12's mechanism predominates because it is faster"... Think about it: Since you have no experimental clue about the correctness, or indeed the relative rates, of the two mechanisms, as stated your argument is just circular reasoning and I could rephrase it with "I think it's the fastest because I think it's the fastest".
Thanks for clarifying your question. First, let me reiterate that I favor something similar to what's in post #16, but I haven't completely disregarded the one from post #12. If only, as I mentioned before, because Padwa himself included the mechanism from post #12 in his papers, I'm willing to not completely eliminate this mechanism.
That being said, there is, in my opinion, plenty wrong with the mechanism in #12. My main points though are that it doesn't make much sense in terms of electron-pushing and that there are very few (any?) precedent for this kind of decarboxylative process. By comparison, the mechanism in #16 has a very intuitive electron flow and has solid background in the decarboxylation of beta-keto acids (here a vinylogous variant.)
By the way, I'm just trying to entertain this fun discussion here: I know you are very knowledgeable so please don't be insulted if any of this sounds like I'm lecturing. I'm just trying to make it as clear as possible for anyone who may be reading.
As a note, if you look at the experimental section of the article, the reaction is conducted in refluxing DCM for 4 hours, with a huge excess of the very strong TfOH. Yeah, it's very strongly acidic! That being said, as you mention it doesn't matter in a mechanism what the most basic site in a molecule is. Whether the O or the N is more basic is irrelevant: if you can protonate it even to a tiny extent, it may be enough to funnel everything toward product. That's how most acid-catalyzed carbonyl condensation chemistry works: a tiny amount of the C=O compound gets protonated, and that's enough to get things going. But to come back to the problem at hand: the nitrogen is really not basic as it's part of an enamine and it's very unlikely to get protonated.
Why do I say that the mechanism in #12 has weird electron flow? Because of microscopic reversibility arguments, a mechanism has to make sense in both directions. If you look at the reverse of #12, it involves the quite cringe-inducing nucleophilic attack of an enol on the oxygen of CO2 (!), together with the carbon of CO2 acting as a nucleophile (!) and attacking an iminium ion.
The reverse of mechanism in #16 is completely well precedented and involves attack of an enol on the C of CO2, followed by an alkene addition reaction under strong acidic conditions. Also, if the alignment is ok and if there is a carbocylic acid intermediate, you could potentially invoke a vinylogous ene reaction to form the acid (i.e., the decarboxylation of a beta-keto acid is a retro-ene reaction.)
For the mechanism in #16: If it is, as pictured in #16, a concerted process, then the incipient aromatization should increase the acidity of that hydrogen just as it does in #12. By the way, it could very well be concerted. If you look at the molecule in 3D (I just minimized its structure in ChemBio3D Ultra), you can see that everything is really well aligned.
If it's not a concerted process and you first form a carboxylic acid: Protonating the top oxygen makes the carboxylic acid a very good leaving group. Then everything is perfectly aligned (H and O are stuck in a perfectly antiperiplanar conformation) for an anti elimination with one of the H's of the methylene group. Furthermore, this elimination relieves the tension forced in by the bicyclo system. To say it differently: I would not expect this elimination to be very difficult, especially with an excess of TfOH in boiling DCM!
This is a fun mechanistic problem. Let me know what you think!