Long story to address all your options!!
I just built a new Rifle using an old custom Hand Cut Rifled barrel from Ron Pence. This 27 1/2" blank was pulled about 20 years ago, the throat gone and coppering so bad it couldn't shoot a 1 1/2" 3 shot group anymore, forget cleaning it, that was a day long job.
So I didn't have a rifle to put it on if I had it cut and rechambered, so had Fred Moreo at Sharp Shooter Supply scope it and tell me could we make it shoot again, since Pence will no longer build his hand cut barrels. Fred said we get rid of the 4 to 4 1/4" alligator back, he thought it looked useable.
I found a Savage Axis, gave $250.00 for it and took both to Fred, bought an unfinished birch laminate from him and he started the rebarrel cut and chamber. The new rifle had a 22 1/2" finished length in 6mm BR Norma, shoots 1/4 moa and a great Varmint rid. So we have established even a shot out barrel can be reserected!
Then 6 months later I bought a Stainless 30/06 Axis in another Tupperware modular stock to build another rifle, a 27 1/2" 6mm AI to build another 6mm AI to replace the 20 year old Pence rifle I had years ago. But, the first rifle came as 243 Win. I had a great idea, while Fred builds the new gun, I'll have him rechamber this 243 for a fire forming barrel,,,,,,, woops! After forming a 100 rounds of Lapua 8x57 I formed into 5mm Remington I found some old ammo, 80 Berger's from 20 years ago that were from that old Pence build, so I decided to see how it shot,,,, This was the result, as well as shooting 85 Sierra HPBT game kings under 3/8" at 100 yards, 80 grain Sierra SBT Varmint under 1/2" @ 100 yards, 100 grain SP Pro Hunter Sierra under 3/8" @ 100 yards. Those 80 grain Bergers I had to seat .050" deeper for this new 6mm AI chamber I had cut on the factory barrel, but 1/4" moa that holds to 200 yards shows how good a factory barrel can shoot with a little 1/8" cut off the chamber and a new improved chamber cut.
What I am saying is this, it would be cheap to have that rifle rechambered, and I have seen how good a factory barrel will shoot doing this if it still has a good throat, I also seen how well a shot out barrel can shoot when it is long enough to establish a new throat, even if it's not perfect.
Fact, you have a good action! that barrel could perform great with an improved chamber. You have more to work with than I did, on both accounts. Your action is already in a useable stock and bedded, that won't change. I say time to find out and save a bunch of money. and have a rifle you like shoot the way you intended it. your choice, how deep are your pockets?