What about Rhodesian Ready?
Not that the Rhodesians have any great rep for carrying shotguns, but why wouldn't the Rhodesian Ready (there really is such a thing) be a better long-term carry than the standard ready?
OTOH, moving a rubber covered buttplate up across heavy clothing to a ready position, such as when wearing a winter parka, seems to invite "snags" unless you do your dry fire mounting wearing a big michelin man coat or push out anticipating the extra bulk.
Due to the amount of Afganistan stuff on tv, I'm now wondering if the classic AK47 Afgan Irregular Raghead Ready might not be a good idea for those of us who have full-stocks with pistol grips. It is sort of like the Rhodesian ready except the buttstock is resting on the forearm, ready to be driven by the PG hand and whipped into the shoulder socket on demand. Eight zillion AK47 slingers might be wrong, but is is worth a look?
Edited to note that I'm only talkin' about Serious shotgunning here, not trap or clay or whatever, which I know nothing about.
My guess, of course, is that any real Serious shotgunning will be done without any sort of name-able "Ready" stance other than... "Ready, babe?, OK FIRE!" or at least for those of us lucky enough to be sleeping with our shooting gal.