Feeler gauge isn't going to work. It is hardened and ground to size, and resists bending and being attached to anything. Shim stock is milder and softer, and will work better.
Plain, old typing paper will take up .003-.004 of even, or uneven wear, as will a simple little rectangle of brass sheeting, available at hobby stores. A drop of oil doesn't hurt on either, but, inspect and replace the paper method on occasion. There was an article in the Double Gun Journal about a gent that had used a Nitro Special with a brass shim as his duck gun, using loads he wouldn't use in his good guns, for decades, with good results.
If I had a "Name" English gun (I have in the past, and don't anymore, by the way) I might not fix it this way, but, only because it would likely effect re-sale value. That is the cross you bear with a pricy gun. But, most of the guys here who bring up collector value, and mock low buck repairs really wouldn't know a collector gun if it shot them in the ass-look at any of the Parkers or Winchester model 12s on the auction sites and prove this to yourself. Most are worn out junk, with big prices on them. This same group will happily advise you to make a $400 repair on a $250 gun that will be worth $250 when you are done. A model 24 is just such a gun, and you will be better served by using it, with a low dollar repair, rather than throwing money at it.
Good luck, by the way. There are plenty of steel barreled, older, entry level double guns that could be back in the field with a bit of help on their loose hook. It doesn't take a master machinest to do it (you can do it that way, but, why?) just a bit of ingenuity.
Best,
Ted
