Lowrider, if you were to change from an amp having a single-ended internal signal path to a fully balanced amp I would expect that the differences in the intrinsic sonic characters of the two amps, and perhaps also differences in their interactions with the particular speakers, would most likely greatly overshadow whatever difference may result from providing that amp with an unbalanced vs. a balanced input. Also, my guess would be that finding a fully balanced preamp providing sonics that are as much to your liking as those of the UV-1, for a comparable price, would be a tall order if not impossible.
Regarding your mention of impedance differences, many amps providing unbalanced and balanced inputs connect the center pin of the RCA connector directly to one of the two signal pins on the XLR connector, usually the non-inverted input on XLR pin 2. When the RCA input is used in those cases the unused signal pin on the XLR connector is simply grounded, via either a jumper inserted into the XLR connector or via a switch on the rear panel. And in those cases the doubled impedance that is usually specified for the balanced input, compared to the unbalanced input, simply reflects that the balanced input spec is based on the sum of the input impedances of the two balanced signal lines. So in those cases connecting an unbalanced signal to the XLR input via an adapter, for example, would result in the same input impedance as connecting the unbalanced signal to the RCA input.
Best regards,
-- Al