That seems pretty deep in the hole to me for 340 pistons.
But you'll need to know the volume of those J heads before you go any further. If they've been milled to work with those pistons you may not have to do anything, although .065 in the hole isn't exactly ideal as far as setting up your combustion chamber goes. But if the heads have been milled down a bunch you may already be at 9:1 or better depending on the head gasket.
Here's a compression calculator that seems to work pretty well.
http://www.kb-silvolite.com/calc.php?action=compYou'll need to know the volume of chambers on the heads and the piston volume (do the pistons have valve reliefs?)
For example, using the above calculator, if you have 65cc heads, a 6cc piston volume (usually 5-7cc on 340 pistons with valve reliefs), have pistons .065" below the deck, a 4.15" bore on the head gasket and the .024" gasket thickness you posted, you'd end up with a static compression of 8.8:1. But that assumes the volume of the heads and pistons, and small changes make a big deal. J's ran anywhere from 65-72cc's, so the actual volume will make a big difference. If yours are 72's you'll only get 8.2:1 with the same specs as above.