If I understand your project correctly, you are going to sleeve a breechloading 10 ga double, converting it into a quick twist muzzleloading gun. The liners will be breeched. Are you going to leave the firing pins intact, and have them strike #209 primers set into the breechplugs?
Your liners will be turned to match the chambers of the gun, and then reduced to be a slip fit into the existing bores?
If both the liners fit the original bores exactly, I don't think there is any chance that the regulation with saboted bullets will be satisfactory. What calibre are you contemplating?
I would suggest that one barrel be lined with an immovable liner. For the other, have the breech end a good fit, but the rest of the liner slightly smaller than the 10 ga bore. Then you could wedge, shim, use eccentric bushings, whatever, at the muzzle, and have a chance of getting the barrels to regulate.