Yeah I looked at the SRP's and the CH is .036" lower than a standard 340 piston so that is not promising. Same goes for the Ross pistons. I'll keep looking. BTW, do you have to use stock rods and crank?
Some lighter flattops that would work are the KB 243's; usable off-the-shelf. The 1.840" CH is the same as the stock 340 pistons. Mill the block's deck to a deck height of 9.565"; IIRC that is quite safe but check that out. Then the KB243 pistons will stick up .053" above the deck and with the .027" head gasket, you will be at the 11.8-11.9 SCR range. The KB243 weight of 720 grams piston + pin weight is a lot lighter than the stock which is around 873 grams piston + pin. You'll take weight off the crank to balance these.
These KB's are hypereutectics, not forged, so keep that in mind.
And Hughes lists some Icon FHR's that would work and are forged, but they list a piston weight of 724 grams. I cannot say if they are listing piston only or piston + pin weight. These are not in the online catalog so that weight number that bears checking. (I think 70aarcuda knows but a quick call would do it.) The eyebrows are 7 cc's so the CR will be a few tenths lower.
BTW, I recall another piston MFR being mentioned that does custom variations for a lot less than $1000. Dang, wish I could remember the name.