More on this:
All lines to/from the RRC are now choked with Mix 31 toroids, along with all interconnections between the K3 and the KPA1500, and on the output of the KPA1500.
The problem is even worse now, I can't use the amp on 40m at all because the AGC is so unstable.
I did try different software, and interestingly enough using MMTTY on DATA A-AFSK the problem goes away. But (thanks to a tip) it turns out that if I set CONFIG:AFSK FIL=OFF (no DSP filtering of the transmitted RTTY signal), the problem reappears. This must be a clue but not to me :-(