What's with the medals on this forum?

[worldofneil]

There are posters here with two red medals but < 2k posts

That means one or both of their medals are "kin" medals, not post count medals. You can confirm this by selecting/highlighting their medals. The post count medals are a single image on the right side of the medals.

less popular posters such as myself with well over 1k posts but only one or perhaps no 'kin' medals at all.

You have one gold kin medal, the other gold and four silvers are your rank 9 medals (for having between 1000 and 1999 posts). In 40 posts time (at the time of writing) you'll have 2000 posts so you'll get rank 10 which is two gold medals, so you'll have 3 gold total. 1 kin + 2 post count.

Because of this possibility, I am not sure if your test can pinpoint acquirement of kin based on likes alone. I think we would have to test multiple accounts in order to eliminate other possible algorithms.

Possibly, although since that post I select hasn't post on the forums since 2015 it's quite probable that they don't read the forums at all any more (so the only action that would be happening would be other people liking their post).