Pivoting from 340 to 360

I'd just run a flat top piston and let the compression fall where it may. Prob will be a measured 9.5:1 or so. Don't waste time trying to build for quench or using the deflector/quench pad pistons with a cast iron head and no blueprinting. Keep the camshaft in the area you listed. I'd use a Comp but that's me. Get springs to match the camshaft - and be aware a lot of the purported .904 lifter designs need true dual springs so the spring seats and guides will need attention on the heads. (one of the big reasons I'd steer clear of them - you don't need it and you won't feel any difference) I agree - stock stamped rockers are fine assuming the camshaft can work with them (doesn't run lifters that needs adjustable valve train).
Agree 100% for budget build. Just using the flat top KB107's or H116's will get you up to the low/mid 9's for SCR if you use a .028" thick Mr Gasket 1121G head gasket; that is a FAR cry better than the stock SCR. Pushing 10:1 SCR with no quench and open chamber heads and no detailed set-up in a heavy car is problematic.

KB's are not stock piston+pin weight, so I'd go for sure with the H116's for budget; they are stock piston + pin weight and so no crank re-balance is needed.

The KB373 quench heads are interesting but take some head milling to get to a quench gap and some fanagling around to balance the head milling and chamber size for the right SCR, so are not what I'd consider 'budget' and 'ready for assembly'..... and they are not stock piston+pin weight.

BTW, when you install the cam, time it properly, and find the ICA (intake valve closing angle, measured in crankshaft degrees, at .004" lifter lift on closing). If you get it into the 62-65 degree range, you dynamic compression ratio will be pretty good for a budget build. If it is waaay off from that installed dod-to-dot, then I'd do a complete cam timing profile (durations at .004" and .050" lifter lifts, plus intake and exhaust lobe centerlines). Hughes don't give you 'advertised duration' numbers on their cams. So you are kinda in the dark as to DCR.

Can you give us a cam PN? That, and it's timing, are gonna determine a LOT of how your engine will run and behave.