How do I tell if my 340 is internally balanced?

All the above is right. Pix of the damper please.

The TRW's are not typically lighter than stock but are stock weights. So it is doubtful that this engine is correctly balanced if the damper is not the correct one. The external weights at the damper and TC used for the later 340 are significantly smaller than for the 360's, so this might not have much vibration in the butt-o-meter with the wrong damper. But it won't be doing the crank and bearings any good.