When I ordered aload of cartridges from Gamebore this morning I mentioned your delema. The very helpful young lady say's that Gamebore operate in the US under the Kent Gamebore brand. She say's they load a 20 bore low recoil game cartridge specialy for the US game market. It is a 30g (1 1/16 oz I think) No 5 shot load and it is called The Hushpower. 30g does seem a heavy load for a low recoil 20 bore load but Gamebore produce some excellent cartridges and as I said before their 28g subsonic has far less recoil than the equivalent 21 g load. It does rather seem to defeat Newtons laws of motion!
Obviosly I have never tried these as they are a US product but if they are soft enough they should certainly kill well - possibly worth a try.