I am a trained electronic tech with experience of over 50 yrs...I have serviced scopes both vacuum tube ,analog and digital for many years...as far as the controls...no the waveform do not reach the far left or right horozontaly but vertically it goes all the way up or down. The horz sweep is fine and matches perfectly with another unit I have that functions perfectly. I'm beginning to think there is an issue with either a dirty trimmer or worse, the hv anode supply. I will post a screenshot soon.
That's a more useful characterisation of the situation.
I presume the vertical deflection is roughly correct, since you don't mention anything to the contrary.
I presume all the PSU voltages are correct, since you don't mention anything to the contrary.
Since the beam can reach the top and bottom of the screen I doubt it is the HV supply.
In that case it is only the horizontal calibration that is faulty. Follow the procedures on p4-53 of the service manual.