Yea, to parrot what's been said, my understanding (albeit superficial) is that the benefits of running a balanced system is all or nothing -- you either run 100% balanced or you're effectively not at all. Put differently, the signal either is or isn't balanced from start to finish, and switching up connectors in the stream doesn't change a thing.
Far as I see it, the only reason to ever use a converter is when you've got two components that otherwise wouldn't be able to talk to each other. For example, my preamp has XLR inputs only for the HT bypass loop, but my HT Receiver is single ended only. Thus, the only way to plug the two into each other (preouts for the mains on the HT Receiver into the HT bypass loop on the preamp to drive the main speakers) was to either get some converter plugs or some RCA to XLR terminated wires (otherwise, I'd be pleased as can be to simply run RCA to RCA). Ultimately went with the terminated wires rather than converter plugs (on the theory that it's one less piece of junk in the chain to mess stuff up), but, either way, it's a 100% single ended feed 'cause, once it starts that way, that's how it stays.
So I'd have to agree, even if you found the perfect sonicly neutral converter/adaptor (which might itself be a mythical beast), it likely wouldn't be worth it as you'd simple be plugging into a different hole, not changing the nature of the signal. Or, at least, that's how I understand it. Meantime, enjoy.