Exists yes, available not really.
Wanstalls did a limited run of 12" 12 gauge from Yildiz of Turkey.
Not what most would consider high quality but well above the other options in a short barrel length.
"Does such a thing exist?"
No, quality gun makers avoid this sort of thing in their lines, as they are utterly useless for wing or clay shooting. The shortest, quality SXS I can think of would be a Churchill XXV, they were made for drive grouse shooting.
No they won't. H&H and other British makers have been known to turn down requests for guns they felt didn't reflect appropriately on their brand. I've also seen Spanish makers not grant a request from a buyer for similar reasons. The Turks however will make you anything.Holland and holland will make anything you want. Give them a call.
Yildiz.....Corwin......"High End"
Which of these things is not like the others?
This is definitely my morning chuckle.
Most high end douchey shotguns with fancy etchings and endangered tree wood tend to have 30" pipes on them.
No they won't. H&H and other British makers have been known to turn down requests for guns they felt didn't reflect appropriately on their brand. I've also seen Spanish makers not grant a request from a buyer for similar reasons. The Turks however will make you anything.