Not sure why the Krell manual states that both should not be used at the same time. It looks like the traces on the board just connect the two outputs together (like a Y-splitter cable) as shown in the upper left part of the following picture:
It may be an issue with driving two different types of amplifier impedances, not sure. The other alternative would be to use a Y-splitter cable, which is doing the same thing and you have multiple cable connectors that are degrading the audio quality. I say that you should just try connecting both XLR and RCA outputs and see how it goes.
I suppose you could use the RCA input/out of the Polk subwoofer to connect on to the Bryston amp, but you'll definitely be losing sound quality here.
If you have any interest, I would be willing to do the re-cap job for the cost of the components plus shipping plus $100-150 labor (depending on what you wanted done). It's probably a couple hours of work for me. If you don't have a good desoldering gun, it can be extremely difficult to remove solder and dis-attach the capacitors. It is easy to pull up traces on the circuit board if you are not able to melt the solder enough - and you've just destroyed a $1000 item. lol. Sometimes you have to re-apply new solder and re-melt the contacts to get all the solder hot enough so that it lets go of the capacitor leads.
Oh, expect to have a burn in time of about 250 hours with those Muse capacitors.