Yesterday, in the middle of the day, we had a situation where the KvF arena said 0 feds, 30 klingons. My proposal would simply merge KvK, KvF, and FvF queues. You'd still have a strong possibility of getting FvF simply because there are so many more federation players in the first place. It wouldn't be just FvK. Of course, that would change if there were more Klingons.
I usually queue for FvK. If for some reason I'm not queueing for FvK, I don't want to do it at all.
Queueing for both, I seem to hit a lot more FvK queues when I would most want to avoid FvK. It's probably because other people are trying to avoid it at that time too.
I sometimes avoid FvF too, usually if I get stuck in back-to-back PUGs faced off against partial or full premades from one of the better fleets. I guess because our matches end at the same time and we queue at the same time, we keep facing off against the same people. Sometimes it helps to only queue for one side or the other to break the cycle.
Lately I've been avoiding FvK more. Sometimes it's fun, but when it's not fun being forced to do it anyway would only make it worse. I feel bad for KDF players, and my klink is mostly retired because of the queues, but you can't expect people to do something they don't enjoy. In FvF at least I know that balance issues have nothing to do with the results, and I usually enjoy the fight even if my side loses horribly.