Don't know what you paid for the engine but you are looking at the cost of a rebuild. How much is the seller willing to spend?
A 340 block bored .040 is getting a little thin, especially if there is any core shift in the casting.
Sonic check the bores first. Magnaflux the block/crank.
If this is your first engine build, pass on trying to go the economy/DYI build.
Too many things may possibly wrong.
Especially when buying any "rebuilt" engine is a crap shoot to begin with, No way of know what quality of job was done before. and not having the experience and all the proper tools and knowledge can end up being very disappointing/expensive.
Get an estimate to make the short block right and deduct that from the buying price. If it doesn't work out, you would be better off to pass and keep looking.
I have seen several 340 blocks and engine listed lately.
If being "correct" is not a factor, get a 360 or stroker.
Same money as building the 340 and engines are already built, ready to bolt in.
Mopar Small Block “LA” Engine: Bore & Stroke Chart