Double 30, You kind of have me confused at the first part of your idea, but if you wanted to put a 45 ACP barrel inside of a 12 ga. barrel that can be done. First off I don't know if it would be legal with the inner barrel being only 10" long ? I'll leave that to someone more up on firearms law.
You do not need to bore out the 12 ga. barrel to do this. You will need a 45 barrel blank that is a minimum of about 7/8" dia. to start with. Take measurements of the shotgun barrels true bore dia.
the chamber dimentions, forcing cone ect. Turn your barrel blank to .004 to .005 under the diameter of the chamber and bore sizes and leave enough diameter at the breech end of your blank to have a rim like a shotshell, when you get it to fit into your shotgun barrel where it's snug but doesnt need to be pounded or pressed in and stops flush with the breech face of your shotgun barrel your done with that part. I'll leave it up to you if you want to chamber your blank before or after glueing it in the shotgun barrel. The way I have permanently joined the two barrels together is I use a 2 part epoxy with a 3500 PSI bond strength, clean both barrels to get a good bond , then I take length of threaded rod 1/4 20 or whatever fits your need and tape over the threads so not to scratch your rifling stick it thru the rifle blank and at the breech end use a flat washer and a hex nut and at the muzzle end the same thing but be sure your washer has clearance to go thru the shotgun bore without interference and leave the threaded rod long enough to extend out past the end of your shotgun barrel. Tape up everything on the outside of your shotgun barrel with painters tape to keep from getting epoxy on your bluing or anywhere you don't want it. With the epoxy I use you have about 15 minutes of working time so have everything right in your mind before gluing.
You will need another flat washer that is larger on the OD than the muzzle end of your shotgun barrel and a hex nut to use to pull the rifle blank into the other barrel when you have the epoxy on it takes that mechanical pull of the threaded rod to squeeze out the excess epoxy and to be sure you get the liner barrel flush at the breech before the epoxy starts setting up.
Thats the process that I have used sucessfully many times, after that I will leave it up to you as to making the extracter / ejector work for you. I hope this helps, but not sure of the legality of it ?
Jedman
Something I forgot to mention, I coat the outside of the rifle blank and the inside of the shotgun barrel both with the epoxy before joining them. A cleaning rod with a wool bore mop or something similar works for applying it to the bore of the shotgun barrel and a small brush to apply it to the OD of your blank.