Stock high compression 340-Max cam lift?
Correct. So would the Lunati 60404 be too much cam? Also what lift is the stock 340 spring good for?
The stock springs WILL NOT work. Not enough seat pressure for a 60404, even if they weren't 40 years old. Lunati also recommends dual springs on all of their cams. That said, I found a set of single springs with a damper that meet the seat pressure needs. You'll also have to pay attention to coil bind when selecting the springs for the 60404.
I have a '68 340 that I rebuilt with 308 heads, 2.02/1.60 valves, KB 243 pistons (.060 over), and a Lunati 60404. Although I haven't fired it yet (one of these days it will be in my Challenger), I didn't have any valve to piston issues. Pistons are .018" over the deck, just like Ma mopar actually spec'd (most probably aren't quite so far out). But, the valve pockets on the 243's are quite a bit deeper than on a stock 340 piston.
If you're taking the heads off and having them ported, measure the pistons to the deck and find out what you're dealing with. And it'd be a good idea to measure the valve to piston clearance with some clay to be sure its right. With a smaller cam you might get away with using some stock components, but with a 60404 you're going to need new springs, and I'd recommend an adjustable rocker set up as well. Its a lot of pressure and lift for the stock stamped rockers to deal with. Also, is your car an automatic? If it is, you'll need a higher stall converter too. Lunati recommends at least 3.73 gears as well.