How do I tell if my 340 is internally balanced?

Well, we would need to qualify the statement of 'pretty smooth' LOL. The stock TC and flexplate of the '76 Cordoba would certainly not be set right for a cast 340 setup; I looked, and the only engines originally in that car would be a 318, 360 and 400..... the 1st takes neutral balanced external parts, and the 360 takes a much heavier external weight than the cast 340. IDK on the 400.

It is theoretically possible that the heaver external 360 weight might balance OK with heavier TRW pistons inside the 340, if one was darned lucky. But then the neutral balance front damper would make zero sense.

Exactly. One person's "pretty smooth" can be just wrong as heck. lol