How do I tell if my 340 is internally balanced?

A little bit of speculation. ---- The harmonic balancer was likely thrown on at a later date. The paint doesn't match the engine. There is no Mallory metal that I can see. I do see small holes in some of the counter weights, and a 1/2'' hole in the last one. A sign that the crank was rebalanced at one time. SO, my guess is that the crank was balanced with the proper harmonic balancer and flywheel.

I'd pull #1 maincap and #1 rodcap and plastigage. If good, add the correct harmonic balancer and B&M flexplate [340/727 #10235 ?]. This assumes you have original pistons and crankshaft.