Al can tell you the whys you will need balanced cables over single ended for the lowest noise floor possible.A properly designed balanced interface will reject nearly all noise that is present equally on its two signal lines, since a balanced receiver circuit responds essentially just to the difference between the voltages on those two lines. An unbalanced interface has only one signal line, of course, so it will not do that. Also, a **properly designed** balanced interface will be less susceptible to ground loop-related hum and noise than an unbalanced interface, since a properly designed balanced interface will not put signal current through the ground connection in the cable. Although as was said earlier it appears in this case that a ground loop is not responsible for the problem.
A suggestion that occurs to me at this point, although it is just a hunch: In addition to obtaining longer XLR cables, purchase some RCA shorting plugs and insert them into the amp’s RCA input connectors, while connecting the amp to the preamp with the XLRs. Just a hunch, as I say, taking into account that both the specs for the amp and the Stereophile measurements at the link Jim provided make it clear that the amp’s RCA and XLR inputs are received by separate and independent input stages. (If that were not the case shorting plugs on the RCA inputs would probably short out one of the two signals in the balanced signal pair).
You can find a number of sellers at eBay offering inexpensive RCA shorting plugs.
Regards,
-- Al