Let me jump back in. Interesting topic. I've had a couple of 327s - one in a '55 Chevy and one in a '63 vette. I rebuilt both, the first with lots of help long time ago and the other just recently.
If the heads are old style, the valve stem seals a like rubberbands in size. You might need to machine to have new seals fit.
Without measurements you really don't know what you've got. Valve stem clearance could be too great. Oil ring gaps wrong and/or in wrong position. Bad bore. Out-of-round hole(s).
Crankcase ventilation problems? Rings not seated yet - just one hour of break in?
I guess the big question is - does it hurt to drive it? Well, if you're not worried about an "original" block in your car, then you don't have that much to lose. There are blocks everywhere to buy. I really like the 350 idea for a lower budget replacement. Sky's the limit. So, I'd say drive the car. If it is just rings not seated yet, then that will clear up. If the engine builder put the rings in wrong and too much oil is "hanging around", then it's just oil and your pride!
If you can do your own work, pull the motor and go back through it. Let a machinist mic all cylinders and evaluate the heads. (A step approach would be to pull the heads and leave the motor in the car. Have heads evaluated. If valve guide or seals problem, fix and put heads back on!) If heads look good, then mic bores while motor is still in the car. You might find out-of-round condition. If so, maybe now is the time to buy that block...)
What does everyone else think?