for a 'survival gun' id simply go with a lightweight .22LR. a 12ga is
heavy, especially when you factor in the ammo.
if you are dead set on carrying a shotgun, and you want something short and compact, an 8.5" Grizzly with a short LOP stock will be right at 26" and yet retains full functionality.
IMHO PGO shotguns give up far too much in functionality. folding stocks all have their issues - i have yet to find a folding/collapsible stock that is as solid, gives as good/consistent a cheek weld, and is as comfortable to shoot as a traditional stock.
at the minimum 26" length, you can either have an 18" barrel and PGO stock, or an 8.5" barrel and a full stock. personally, id
much rather have the latter and retain the shotgun's full functionality/versatility. PGO shotguns are ideal for LEO/MIL breaching, or as just something different for some range/plinking fun, but IMHO they are ill-suited for any defensive role.
with a cylinder bore, an 8.5" barrel has noticeably more spread with shot at even short ranges (~15 feet). depending on your intended use, this may be a good thing. if not, then you can have the barrel threaded for chokes - there is plenty of meat in it. slugs with a short barrel and bead sight arent the most accurate, but you can remedy this by installing aftermarket ghost rings.