Since both channels are equally affected the fault must be either in the beam switching circuitry (not very likely) or in the Y amplifier stages following the beam switching.
There is a fairly simple test on the beam switching that you can do with just a DMM. If you locate test points TP364 and TP 374 on schematic <3> and the example waveform shown in <21> and <22>, you should be able to replicate the DC values ( +1V and -1V) by setting the horizontal mode to ALT and the timebase to its slowest setting so the voltage flips every half second or so. Set both traces to somewhere near the middle of the screen and trigger to AUTO. This is not a definitive test but if these voltages are wrong the diodes may not switch correctly.
I only just now noticed you have Trig View option on the 465. Try feeding the calibrator signal to Trig In, set Trig Source to Ext or Ext/10. Push the trig view and you can move the trace up and down with the Trig Level control. Does the vertical height of the displayed trigger signal change with position in the same way as do the Ch1 and Ch2 signals?
If Q322 and Q324 are socketed then remove and test them. The Service manual schematic <3> shows various voltages around Q322 and Q324, set up the scope as best you can to the conditions defined in the manual at the start of the Schematics section under the heading 'DC Voltages'. See how well your measurements match the figures in the manual.
Farther down the Y amplifier chain there was a change from discrete transistors to an IC based Y amplifier. Which one do you have?