Springfield M1A National Match
Adding a Springfield mount and a Vortex Viper PST 4-16x50mm scope.

How do I determine the correct height of my scope rings? - short of buying something, figuring out if they are the right height, and exchanging them until I get the right height so that I can use the iron sites under the scope -

Any assistance appreciated.

If you insist on using the iron sights you're going to end up with scope rings too high to get a good check weld on the stock.

Most everything I have read says that you should avoid using the Springfield mount.

Sadlak and Smith Enterprise are the 'go to' sources for M14/M1A scope mounts.
Another source is the CASM from our neighbors to the north at M14.ca

I would think medium rings are the lowest rings you could use, but tall rings may be required for a 50mm objective.

Ameshawki is spot on... start shopping for a cheek riser.

I have an M1A NM with an Enterprise scope mount, and the Springfield Gen2 4X15X56 scope, it won't matter what the objective size is because the scope mount won't extend far enough to the front to be affected by the objective.