Why not build a 340?

The hurdles for 340's are the block cost and fewer piston choices; the 360 has the advantage in both of these areas. In hydraulic roller use, the 340 blocks' lifter bore chamfers can be problematic, but that is not likely your issue to deal with.

In your case, the 360 will have added cost in a different crank and different front damper and flextplate/flywheel. With a 340 block, you can drop in your 318 crank and reuse your flexplate or flywheel, and reuse the damper if it is good condition. Also, IIRC your 318 pan will fit right on the 340 block but not on the 360. So parts re-use will be better for you unless you find a complete 360 short block (should be do-able).

What HP range are you looking at? If under 400 HP, then the cast cranks are supposedly safe.

Stock type 340 pistons for the earlier years set about .018" above deck; this is as opposed to 318 piston setting something like .080" below the deck. So managing the increased CR with those smaller chamber 318 heads is going to have to be solved before you make any final decision. Some options are different pistons choices and a thicker head gasket. If you get this solved for the 318 heads, then you ought to also look ahead to whatever larger heads you are considering, to see if they will drop the CR too low. I think this can be managed with head selection, maybe some milling of the later heads, and changing head gaskets thickness, but I would plan it out now so there is not an unwelcome "Ooops!" moment later.

All of this can be worked out it is a simple math problem and there are plenty of calculator around to make it easy.