340 engine oil consumption ???
1. Start with the PVC valve. 2. Since the engine sat for so long, it could be the rings are stuck to the piston lands. Run a good crankcase flush through it a couple of times. 3. The valve stem seals could be part of the problem.
I have the same issue with my 67 273 stocker and I just changed the valve stem seals. My next move will be a cylinder treatment with help from one of the experts on this site. Sounds like a great car/engine combo. You will have a lot of fun with it until you pass it to your son's friend.
Best of luck with it, Rat