because of the differences you cite, seem to engage using the statistical approach (vs. the "matched" units approach) only in their Model 7, where their criteria do still differ from yours, as you point out:

(Mech article, p.25 in .pdf)
Interestingly, REGIME only reaches statistical significance in the post-1945 era ~Model 7! and is negatively associated with incumbent victory, suggesting that as states become more democratic their vulnerability to defeat increases. This at once supports and qualifies existing arguments about presumed ineffectiveness of democratic states in COIN wars. To be sure, it suggests that as political systems become more open, the likelihood of defeat is also increased. Yet these shifts in regime type could occur at lower ends of the 21-point Polity2 values—that is, a shift from 5 to a 0—and therefore one should not conclude that stable democracies are especially vulnerable. [71] Moreover, the time-dependent nature of this effect is at least partially inconsistent with claims that audience costs or educated middle classes are hobbling democratic war efforts. Indeed, neither mechanism is exclusive to democracies, nor is it clear why their effects should only be observed after 1945.

[71] We re-estimated Model 7 with a dummy DEMOC variable that denoted whether a state’s regime score was .7, the conventional threshold for being coded a stable democracy, DEMOC was not significant.
This part of the discourse reminds me of many "battles of the experts" in which I've participated - not as an expert, but as the guy who had to translate the expert to the judge or jury. As you know, many of these battles degenerate (from the non-expert's standpoint) into inside baseball arguments between the experts.

What I've gleaned from my experience is that the practical examples weigh more with the non-expert than anything else. E.g.,

from Cavguy
... but bottom line if mech hurts COIN forces than how come 3ACR (has least number of dismounted troops of any BCT in the Army), and 1/1 AD (heavy legacy BCT) were hugely COIN successful ?
because ... da, da, da - and you're off to the races. After reading through Lyall's articles, I can see why you are considering the topic. Bonne Chance.