340 rear main cap

I have a simple solution to your problem, just simply replace the rear cap from a 318, as the 318's and the 340's have the same main bearing caps. I'm surprised that no one else thought of this. 318's are everywhere so locating one should be easily done. I can't believe that none of mopar specialists thought of this.
The main caps are machined and line bored to the block it came from. So yes it could be done but the engine will have to be tore down and line bored or possible bearing failure will happen. He could take the chance but is it worth it.

When replacing a main cap usually the mating surface of the cap should be cut then the cap should be sized to the block bore.