Yes, that is the rod. Probably doesn’t matter but, the serial number on my rod is 26,540. That is a great picture and thread. It appears to be a Heddon , maybe 310 reel. I have that reel and again seems like the reel foot is too wide.
When I purchased the rod , it had a Hardy Flyweight reel on it. Or should I say it came with it. That reel foot is too wide as well, for the fixed end.
Maybe, like you said the cork needs some alterations? Possibly, if the cork got wet a bunch of times, it swelled.
I won’t rush into anything yet! Any more info is appreciated!