You may have already searched but I just took a quick look and Numrich currently lists 6373 Ithaca parts.
For barrels I do occasionally see Ithaca barrels for sale but not often. You didn’t mention the gauge you’re looking for but if it’s sub-gauge Daniel Cote has been gathering orphan sub gauge barrels for years. 800-447-1658
Last year a friend was looking for a Flues forend for a family heirloom wall hanger. I found one for him with Mike Jensen in KC. You’ll likely have to leave a message and wait for a call back but he has a lot of odds and ends. 913~782~6900
I’ll also be glad to keep my eyes peeled.
