What is the modulation transformer you're using?

If it's a mains transformer it could be going into saturation. Proper
modulation transformers are designed to accomodate a d.c. bias through the
windings which normally requires an airgap in the core. In an ungapped
core the dc bias will drive the core somewhere up the BH curve and the
effects will be exactly as you describe - clipping on one of the peaks

I don't have exact specs on it. It's a Stancor, an actual modulation
transformer with isolated secondary so that the RF final could be run off a
different B+ supply if desired. I bought the transformer from a ham who had
pulled it from an AM rig that used sweep tube outputs, and he had assured me
that the match to a 6L6 would be good on both primary and secondary. Perhaps
I can get a mH reading on it with my LCR meter, and someone can do the math
for me.. I haven't used that math in many many years, and it's left me, I'm
afraid.