Ah, I understand now, thanks for the explanation, Pineappledan!
Honestly, I've never been troubled by the supply aspect of captured units. When you play as the Huns, you usually have lots of supply (due to the war weariness, as already noted, and due to going authority (more supply from population) and generating a lot of great generals), you also usually need a few "useless" units to act as garrisons (mostly for Authority) and I'll often use some captured units for that. Also, at worst I'll go over the supply cap by one or two for one turn every once in a while, but that rarely happens because of the aforementioned bigger supply and because it's not hard to leave yourself a bit of a buffer (a unit or two under the cap) instead of always playing at full cap. So I don't the UA ever really hurting me. On the other hand, giving them access to potentially huge numbers of units, albeit a bit weaker, that wouldn't count against the supply cap would be just deadly, especially in human hands. Even being weaker (for example -15 or -20%CS) wouldn't stop me from using them very effectively as free meat shields/cannon fodder (instead of having to use "normal" units for that) and in the case of capturing AI's unique units, their uniqueness would more than offset the penalty, especially considering that, again, it's a free unit. One also has to take into consideration that humans are better than the AI at preserving our units. I mean, we can try this as a modmod at first, but I think you'd have to go quite a bit lower with their penalties (I think at least -35%CS, possibly more, I'd have to think and test it) before you reach the balance level of them being free (supply- and production-wise), and then you'd again be facing the problem of how good the AI would be at using such units, whether it would recognize the need to use them as garrison, skirmish units, cannon fodder etc.
I understand Ekis being a problem due to the abundance of resources and freshwater tiles, so I'm in favour of slightly buffing the Eki (I like your ideas!) in exchange for a small penalty (perhaps temporary, like with captured civilian units?) to captured units.