What is a bare 340 block worth?

Exactly as stated. It's always a balance between how much a potential buyer will pay, and how much you want and how long each is willing to wait for a possible better price.

There are things that IMO only add value in narrow circumstances. These are engines with too many unknowns, especially bought unseen in person. This true whether it is a block, or a built engine. I think the OP has done the right thing by cleaning and checking the block.

A local buyer will always be best, both for getting to see it in person and also because shipping costs will be mentally added by most buyers. But if there are no local buyers, then it might be worth lower costs and broadcasting nationally. Of course to find a person wanting a matching engine to a car, the above is basically reversed.