I have tended to go the opposite direction with the Model 7 rifles. I really don't like the pointing characteristics of the factory pencil thin barrels and of course the short/light bbls don't help when it comes to felt recoil.
The model 7s in 243/223rem and some wildcats with those light bbls are acceptable. But once you get to the 260rem and bigger there really is a noticeable difference. I recently purchased a 22-250 from 240Gord chambered in a Rem mod 7. Lovely rifle with the light weight bbl and quite accurate as long as the shots are kept below three quick let offs in a row. Then the point of impact starts to wander. Recoil, which would be negligible on a heavier barreled rifle, is noticeable but acceptable. For the type of shooting I will be doing with that rifle it will be fine. It wasn't designed to be an extended shooting session rifle for gophers. It is just fine as a coyote or rabbit rifle out to 300-400 yds if I do my part.
OP, I don't really understand your angst concerning the 243 for Deer hunting. I have taken a lot of Deer/Bears/Moose and a few Elk with the 243Win and quite frankly as long as I placed the bullets properly none of the animals would have known the difference from a 338 Win Mag. I have heard a lot of cries of consternation from lots of people on this but I have also proven in the field the it has more to do with poor perception than reality. A gut shot animal is still a gut shot animal and will run and usually wander off some place to die in agony because the shooter is almost always a lousy tracker. Please don't take this personally. That is just an observation I have had the occasion to make to often over the years. It takes a lot of practice and time to become a proficient tracker.
I have a stainless 7-08 with a blue take off bbl. I put it together close to 20 years ago on a rifle that had been wildcatted to a ridiculous wildcat. It shoots better than I can hold it. This spring I found a stainless 24in Rem700 take off bbl that only saw factory proof rounds. I am going to replace the blue bbl with the stainless. My hope is that it still continues to shoot as well. The blue bbl is going onto a Mod 600 that is presently chambered in 308win. That short bbl and excess muzzle blast is a killer for me and causes me to flinch.
I like Remington actions for this reason. Their parts often interchange with little or no alterations.
Whatever you decide, there are a lot of barrels out there in close to or in pristine factory condition that will shoot extremely well.
Even if the switch only makes you feel better, it's worth it IMHO. In some ways it's like getting a new rifle at low cost.