A 12ga. Pardner or Topper goes about 5.25#, and with the Tracker II shooting, for instance, 1oz./1600fps rifled slugs will have about 42ft.lb. of recoil, about like some .375H&H loads. Trust me, a visious kicking beast.
I would choose 20ga., which will still be more than stout; and you will most likely need a recoil pad (I have a slip-on over my factory pad on a 12).
I dont believe you can put the USH on a Pardner frame.
The Tracker II is not that expensive, why not shop around and buy one and not have to mess with barrel swapping, plus you get the recoil pad stock.
BTW, if you did get a barrel fitted, and you should also get a fitted forearm for it, and fitting a recoil pad or buying a limbsaver , or such, slip-on, and shipping you would have almost as much in it as buying one.