The car is almost 55 years old, and the OP said he thought it had been raced and rebuilt. What's the chances that the OE pump is still on there? But no matter what, I would start with a new high volume pump. Why guess with what is on it and what condition it's in? After changing the pump, the OP can decide if anything needs to be done about too much pressure.

IMHO, messing with the relief spring now is a waste of time because it is basically the same job to mess with the spring as it is to install a new pump and it is unlikely that the spring is the cause of low oil pressure. After finding that there is no o-ring on the shaft, I wouldn't put any more effort into that pump assembly. Just move on.