Asylum in Betazed has the worst chances of success and the doffs usually only have two traits, one of them always being telepathic. I wouldn't throw perfectly good Vulcan doffs (Kaas, T'Pel) on that one.
One crit trait Asylums are pretty bad, you get horrible chances at good doffs. Granted, if you have white refugees with bad traits, throw them in there. As for Vulcans, there are a lot of Vulcan white refugees with telephatic, logical, and FF (the exceptions are less than the good ones). Throw those into the Vulcan asylum. For Tellar prime, throw any FF and stubborn since aggressive isn't a bad trait there. For the Andoria asylum, I think there are only 3 good white doffs, one not being from the chain. As far as I can remember Earth only has two. If you get a blue or green refugee from grinding doffs, you're most likely better of selling it for EC than playing the Asylum lottery from it. On the KDF side, each Asylum seems to have at least two great refugees, but since refs are harder to get there, you have to deal with what little is out there. For other Asylums, there is always a good or decent refugee to throw in. Any congenial goes great for Bolians, etc, etc.