Choate sells a 13.5" overall LOP stock (including recoil pad) for the Remington 1100 that can take spacers. My son can shoot it, but he does prefer closer to 12.5" LOP. After installing the stock, I stuck with it, as despite being a bit ugly, the recoil pad makes an already soft-shooting 1100 even softer.
Cutting down a wood stock to 13" is not viable with some semi-auto shotguns. For instance, for the Rem 1100 12ga, 13.5" is about as shot as you can go due to the action spring tube.