Dammit, yesterday morning I wrote up a medium-long reply, then hitting Post got that blasted Gateway Error. Post gone, can't recover it. Then went out for a day bushwalk, during which I got a twig whiplash in the eye, so now will be off to the doctor.
Anyway, briefly: Put this scope in XY mode. Take the cal sig out from this scope, feed it to its Y input and a channel input of another analog scope. Trigger that other scope on the signal. Take that scope's sweep output ramp, and put that into this scope's X input.
Result after adjusting XY gains and offsets on this scope - it's acting just like a scope should, but you have eliminated this scope's triggering and timebase from the display process. Also you have a correct waveform displayed on that other scope, to compare against what you see on this one.