Been awhile since I looked at building a 383.
Shelf stock type pistons look pretty limited to the KB-162 Flat top with valve reliefs, or the Speed-Pro Forged L2315NF30 with no valve reliefs.
The KB-162 has 1.908" compression height and with a 9.980" block height should be about 0.024" below deck height.
The Speed Pro has 1.920" compression height and with same 9.980" block would be 0.012" below deck height.
If you don't want to cut the block the speed pro piston should have about 0.6 more compression ratio.
Example with 0.040" 10cc head gasket and 84 cc heads, KB-162 = 8.61:1 compression, and Speed-Pro = 9.23:1 compression.
If you don't mind milling the block height then at zero-deck the compression ratios would be KB-162 = 9.05:1, Speed Pro = 9.48:1 with 84 cc heads and 0.040" head gasket.
Using a 0.020" head gasket increases this to 9.48:1 and 9.95:1 (zero deck, 0.020" 5cc gasket and 84 cc heads.)
The down side of milling the block is the head or intake needs to be milled for the intake manifold to fit, and likely need shorter pushrods.
Because the Speed-pro piston has no valve reliefs, you would need a mild duration cam to prevent piston to valve clearance issues, but that may not be an issue with a mild build anyhow?
On your stock heads, did you have hardened exhaust seats installed when they were rebuilt?
As mentioned, better flowing heads will really help with making more power.
I may have more info that may help. My old 383 with the speed pro pistons has been sitting on the engine stand for 20 years and I have been thinking of working on it. This may be the motivation I need.