CVA, as to a longer stock, check around on the net, and see if the local smith has any at his shop. You may luck into a good used one for not too much money. The barrel OTOH, you might get lucky on eBay, Gunbroker, or one of the other auction sites, but I wouldn't bet on it. See what the same smith can come up with. My old LGS in NY used to get trade in parts all the time for 870s.
Now, I am not going to say "Don't go that route", but I am going to say that competent hunters and marksmen have been dropping deer just fine with old smoothbore 20 ga. shotguns for far longer than you and I both have been alive. Most of the shotguns used were pretty much as the factory made them, good all purpose firearms that need a few tweaks to become excellent _________ guns. I have an easier, and far less expensive option, that with a little bit of commitment from you, will net close to the same results for about 1 to 2 C-Notes.
Step 1: Find an old J.C. Higgins, Marlin, Mossberg, etc. bolt action 20 ga. shotgun. This is where you biggest savings will be, and since the barrel is permanently screwed into the receiver, it will be a good, solid, base to build from.
Step 2: Pick your sights. The most basic set up is the front bead only, and it is a good "Do most of it" sight. A scout style mount with a LER scope would work well for those who "must" have optics. Your other choice is a peep and post set up. Replace the front bead with a post of the same diameter, and put either an adjustable peep sight or ladder type sight on the rear of the barrel\receiver.
Step 3: Since it is non-rifled, you will need to buy a few different brands of foster style slugs, most likely, all 2.75 inch as the shotguns i listed above mostly do not come in 3 inch models. During your 3 to 5 shot grouping tests DO Not adjust the sights! All you are checking is how tight and where the groups are on the paper. Find your best performer, sight in with it, and stick with those slugs. Practice with them, and make sure they are what you take afield.
If you follow those instructions any deer within 70 yards (irons) or 100 (scope) is on the dinner table after you pull that trigger.
My grandfather's both used BA shotguns for deer (1 in 20, 1 in 12) for over 40 years. I have been using a BA Mossberg 185-d with a Redding Peep on the reciever for 20 years now, and I can say that I have dropped deer out to 70 yards with it more than once but most shots on a whitetail are going to likely be less than 40.
What you have will work. You can upgrade your $300 shotgun for about another $2 to $400 and still have a good shotgun for many types of game. It's your money, and your call. Or, you can go out, buy and older shotgun most would not even look at twice, and build that "antique" into something that puts most modern field shotguns to shame for about a quarter of the overall costs of upgrading yours. Take it from someone who has won several tri-county slug shoots with a 65 year old shotgun, there are few things that are more fun than embarassing thguy next to you in line when he has a $900+ slug gun, and you cut a tighter group with an "$80 Special".