[old_tv_nut]

Which side of the CRT pic is left and right? Trying to correlate that to the voltage on the yoke/damper tube.

I don't know what V15 pin 4 should look like, but I don't see any ringing.
v21 pin 4 looks like a highly filtered and therefore low amplitude signal, which I'd guess is OK.
V22 pin 5 and V23 pin 4,6 both have ringing, which I didn't expect, and I guess that corresponds to the linearity getting wide then narrow then wide then narrow. The problem is finding what is causing (or not preventing) the ringing when so many things are interconnected.

I guess I would try checking capacitors, starting with the bigger vlaues first - C8, 100 uF across the H centering; C89, .1; and also whatever is connected to the circuit, like the line from R11 and R112 that goes of the upper right of the schematic.
Also, do you have any info on what the switch that is lower left of R115 is supposed to do?