my 340..3 cars, 34 years, 1 family. where to go from here

Yes. Condensation is a sitting engines worst nightmare.
I agree that .060 might be a little far. You could have the cylinders sonic checked for thickness, worse case you put a sleeve in it.

I run a .060 340 in our Demon with no concerns, it was originally a street car engine, but is on it's second full race season.

It is a mild build, KB replacement pistons, stock rods/crank, MP solid cam 528/284 & ported 80's model head castings. Shift @ 6500.

8" convertor, 4:30 gear, & 9X28" slicks.

Best 1/8 mile 6.96 / 1/4 mile 11.20 with 60ft range 1.48-1.52

Very nice! I spoke to a local machine shop and it was a very impressive shop, owner gave me the full tour and showed me his equipment, machinery, motors hes working on. I think I will sleeve that cylinder, and go from there.