Really interesting post--thanks for writing it.
I think there's a different line of argument, involving moral uncertainty and option value, that might also favor democracy promotion. The idea is that liberal democracies are best-suited to hosting the 'marketplaces of ideas' where it's likeliest that we'll eventually discover the right moral views (if such views exist at all).
For lots of reasons, we shouldn't be confident that we've already landed on the right moral views. Moreover, it'd be extremely bad for the longterm future if a big portion of humanity locked-in to extremely wrong moral views. So it's important to think about two questions: (1) How can we increase the odds that we eventually identify the right moral views? And (2) how can we decrease the odds that we permanently lock-in to the wrong moral views in the interim period?
With respect to (1): Liberal democracies protect freedom of inquiry and freedom of speech. These freedoms tend to promote the discovery of truth. So promoting liberal democracy will tend to promote the discovery of moral truths.
With respect to (2): Liberal democratic societies tend to allow for ideological pluralism--both in their formal laws and in their cultural norms. Pluralism works against the kind of conformity that could produce a dangerous ideological lock-in. So promoting liberal democracy might also help decrease the odds of a bad lock-in scenario. (Ideological pluralism might also generate a lot of option value by keeping our menu of possible moral views large.)
These arguments are only rough sketches, but, if fleshed out more carefully, I think they might also favor the position you advocate here.