The ENY/arena entry thing might work, but you'd have to add something similar to that for sideswitching to keep people from entering as, say a bish (who are outnumbered), and then switching to rooks (with an ENY of 15 and 40% of the arena population, as examples). But, you'd probably have to do it in such a way that sideswitching wasn't completely disabled, or worked normally when no ENY limits were above 1.
This same idea, or some variation of it, keeps coming up. It does sound like a lot of work, but in the overall scheme of things, anything that makes more people happy is good, right?
Also seems like it might have the benefit of continuing to feed arena totals, which would keep caps up, and let people fly where they wanted, with some limitations. However, there'd have to be a lot more people willing to change countries, and I'm not thinking that's going to happen.