Steve is right about the fill level. With most of us used to modern day radiators, I think many of us do overfill the radiator on our classic cars. I've seen enough coolant on show fields cleaning up after the show to know that!
But --assuming it is not a radiator overheating problem, because that radiator should work fine for your 350-- I have three questions:
1. Have you driven the car enough since the rebuild to get any trapped air out of the cooling system? (It sounds like you have, but if you're leaking water it has to be going somewhere... So just maybe it is air.)
2. I know it is OK, but why are you putting coolant and water? I'd use all coolant, even without AC and even though it wasn't always done that way back in the day. Do anything to keep rust and mineral build up out of a radiator in the long run.
3. A two parter: How old is your thermostat and when was the last time the radiator was flushed? It could be that simple.
The next time it is warmed up --after it has cooled to where you can check the coolant level-- let the car run for a while with the cap off and see what happens.
I know I'm guilty of over kill, but I keep the fluids flushed and changed in my Camaro. Come to think of it, when I turned 40 I had to start doing that for myself...