Just be cautious on the new barrel exchange since as you know if you are into these Model 37® firearms with a serial number below 855,000 have barrels that are fixed and non-interchangeable that would be 1963 roughly and ahead. They can be done but it takes a trip back to Ithaca or a knowledgeable smith
From Ithaca
If your M37 was made before the 855,000 mark (which occurred in 1963), we will be able to furnish you with a replacement barrel for it, but you must send your gun to us for the barrel to be fitted. The process includes machine removal of existing threads, insertion of adapter and re-threading of receiver and re-bluing. Please note that once this is completed you will not be able to reuse your old barrel. Cost for this process is $180.00 for the adapter, plus cost of barrel. Includes re-bluing at no charge.
Also IMO and I own both vintage and the second modern version and although it hurt me bad to pay it initially one can see why they are so expensive now. The old ones were good but these are a much improved barrel design better fit , finish and are a higher quality pump than the old ones they will hold their value like a wingmaster IMO . The old ones which even collectors will not pay a lot for so be aware of that if you are gathering them. I sold two really early corn cob here in the EE about 3 years ago and they were mint. The 16ga finally went for 225 and the 12ga for 250.
There was not a lot of interest Just have a couple of shots of the old 12 I sold or the one I kept I cannot remember since they looked identical side by side. Hard to find much better IMO for their age .Sad but their value has really never increased too much over the years for such a good pump action

Cheers