Just to test fit the barrel, I would place a small piece of shim under the tang. Just a piece of card stock will work. You can use lipstick or something to create a transfer mark, to locate the area that is low. With the shim, in place, put the barrel back in and check for fit. If that works, then you can fix it more permanent with acraglass.
On the other had if the tang is fitting good enough, then I would look at the hook area of the breech and remove a tiny amount from that area to establish a better fit.
Wood can shrink over the years or someone could have switched out the tang or barrel. I have seen tangs, with epoxy placed in the stock, from the factory and it can fall out if a rifle is disassembled. People often remove the tang to drill it out for a peep sight or replace it with one that has the holes already in it.
Final thought, I would not want to pry the barrel down into the channel or have the tang not properly supported.