Did more experimenting . . . problem goes away when bypassing output filters/relays. Connecting antenna directly to pin 5 of T11 works perfectly - gives me 10W key down at 7.050mhz, and about 15W PEP at 7.200mhz on SSB. Bobby dazzler!
The relays I'm using are branded "HUI KE" HK19F, physically and electrically identical to the VRS2H. They look kinda beat-up, but appear to be not used.
Best thing to do is just replace them . . . they're sealed anyway.
I still may need to re-route my RF out path . . . I'll post another update.