Liners are priced by the inch. They run approx $6 (and up) in the size you are looking at.
So for a 48" long bbl, the liner alone would excede the price of a new bbl I believe. ($275/300 depending on bbl length)
Then you haven't figured in the labor & shipping costs back and forth to get the work done.
I'd consider the safety issue too with the ring being close to the breech end of the bbl.
Most bbl are 12L14 and not the most stout material to have undergone overstressing and then put back to reuse. Especially right in front of my eyes, face and fingers. Maybe that's just old, somewhat careful me talking. but something to consider.
I'd fit the 54cal bbl up that you have and use that.
As for the ringed 45cal bbl.
Set it aside for now.
Perhaps the thoughts of reaming it smooth bore and use it that way come to mind (they are actually quite accurate)
BUT, that stressed area 8" in front of the breach tells me NO. Making the walls even thinner by reaming smooth bore, just like the above lining, or rebore-rerifleing would just not be prudent in this case IMO.
If the ring was 8" from the muzzle, that's be a different situation.
I'd simply save what you can of it for a short rifle project or a pistol or two. Elliminating the ringed portion.
..Or Sell it As-Is. Some one will buy it for the right price thinking of the same projects.
It doesn't have to go to waste