When I was choosing a new integrated, I finally resolved my choice down to the L-590AXII or L-509X. I chose to go with the L-509X, but am sure I would have been happy with the 590A.
Anyhow, I noted the speakers reviewed with the amps, and the WhatHiFi L-509X reviewer used the ATC SCM 50 and the KEF Reference 1. There was no mention of the issue you are having. https://www.whathifi.com/luxman/l-509x/review
This Audiodrom review compared both amps and only noted some slight difference between them. http://www.audiodrom.net/en/integrated-amplifiers/detail/31-integrated-amplifiers/574-luxman-l-509x
Advice given previously about your room, may be the most correct, and I fear you could start riding a roller coaster if you change amps. Have you considered a subwoofer? The KEF Ref 1’s are great speakers but can’t be expected to deliver great bass without significant help from the room.
Good luck!