Yeah, clean out that channel, oil it with raw linseed oil to help get some spring back into the wood. Should be okay after that.
Clean out the magazine tube channel with a .50 bore brush or something like that, possibly as big as a 28-bore brush. I think I would use something like Hoppe's for this job.
If you intend to put linseed oil, EVEN raw, into the magazine channel, be VERY careful. The stuff likes to set up like GLUE and then you are scrood, blued and tattooed. If you want some linseed oil in there to preserve the wood, do it the factory way: wipe it in, then wipe the channel clean of any excess, then let her stand for a couple of days. OIL the brass Magazine Tube (after you have cleaned the corrosion and verdigris from it) and slip it in. It SHOULD go in very easily and it should also COME OUT easily.
Isn't that positive cartridge-feed stop just a wonder??? If the rest of the world had adopted that, tube magazines would have remained practical, apart from the change in balance.
Lovely rifle. Looking for some nice photos when she's back on the range!
.