Take what I say with a grain of salt, I'm just not much of a believer in boutique, high end audio cables. I believe a well engineered cable does the trick, and any improvement made by boutique cables is marginal at best. I'll happily take a blind test comparing speakers and amplifiers, but I consistently observe people who put a lot of value in cables refusing to do a blind test. It's ok, I'm not saying there's no difference at all, I'm just saying the difference is small, or the money could be better used.
Anyway, cables made by Blue Jeans cables are good enough for me. So good that you'd be better off taking the money you would have otherwise spent and allocating it to equipment or room treatments.
You can ask Blue Jeans to make you an RCA to XLR cable. All they need to know is that the XLR configuration should be PIN 2 hot. This will let you forget about the quality of the adapter because its terminated XLR right at the cable. No extra bits to worry about, and no worse than the XLR connectors you're already using built into the LS100.
If you are planning to keep the LS100, and you're open minded about a non-balanced amplifier (almost all 300B amps are not balanced), then you don't even need the RCA to XLR interconnects.
Anyway, a few 300B amplifiers on Audiogon right now with varying prices. My favorite 300B is the Coincident Frankensteins (although none on Audiogon right now). They may be more linear than you're looking for, but I have to say that they are pretty spectacular.
If the speakers were even more efficient, I might recommend a 45 or 2A3, but I think a 300B or 845 would be more appropriate. Maybe someone here has experience with those and the Ulysses.