I finally remembered to order the three capacitors I needed for this repair in my last order and so I went ahead and did the repair.
To reach the main board I didn’t exactly follow the service manual: after opening the HP 6634A I just pulled out the transformer and then the main board. Done that it was easy: clean the pcb, solder in the three capacitors and then done.
I also calibrated the HP 6634A… it appears that someone calibrated it without setting up the proper connections on the back. Now it works as it should.