Can you switch your scope to DC coupling? It shouldn't matter at 60Hz but maybe something weird is going on here.
Bingo! It was the AC coupling that introduced the wavy weirdness. See attached.
1st shot: no load, DC coupling, 10X probe across 10K resistor in the L-100K-10K-100K-N divider,
2nd shot: same as above but with 120W load,
3rd shot: 120W load, DC coupling, 10X probe across transformer open secondary.
Note:
(a) alternating square wave seen as expected; see red trace in attachment from my reply #14,
(b) ringing when under load,
(c) duty cycle increases under load,
(d) slightly rounded tops in 2nd but may not be noticeable in 3rd, and
(e) transformer doesn't appear to mangle the 60Hz waveform.
Okay then. I think I've beat this topic to death enough.