The bit you’re missing is that Russia is in one sense a very powerful nation - it can destroy a few thousand American cities with nuclear weapons. That is why confrontations with it should only be undertaken in the interests of the whole American people
I tend toward this position as well, but I also don't view the Russian abuse of their neighbors as anything like morally good.
Digging into what “free” choices Georgia and Ukraine made and what the actual populations of the Territories Russia did occupy want (like Crimea and Ossetia) makes your point weaker, not stronger. The reason Russia was able to hold those places and hasn’t been able to do comparatively well elsewhere is popular support. The copious amounts of US aid required to establish NATO friendly governments in Georgia and Ukraine strongly suggests that their populations were not exactly clamouring for it.
It is interesting that in your model, Russian-backed and controlled governments and threats of Russian invasion are considered the baseline and anything that runs against that is undue Western influence.
Also, the actual popular opinion in Russian-occupied areas is a tiny bit hard to measure and at best is mixed. Russian support is there, but almost certainly overstated given the influence of Russian propaganda, restricted freedoms, and biased polling.
By that 20 percent you mean region never actually controlled by Georgia, but which it tried to invade and conquer?
Post-Soviet Russia directly fueled conflict in those zones, including encouraging expulsion of tens of thousands of ethnic Georgians.
All of these conflicts are messy, but we don't have to pretend that Russia is the good guy just because we don't want to send US men to die fighting for their victims.