Clean out your old mesh with kerosene or gasoline. Let it dry in the sun. Re-oil it and re-install it. The procedure is detailed in the factory shop manual.

Go to the home page of this site and look for Tech Tips. Someone has done what you describe - replacing the mesh with an off the shelf paper filter.

Before I went to that extreme, I'd try to find one of the other types of filters offered on the stovebolt that had a removable mesh filter that can easily be replaced with a paper one like this:
Attachments
IMG_20211031_082455.jpg (83.4 KB, 253 downloads)
IMG_20211031_082514.jpg (94.57 KB, 251 downloads)


1950 Chevrolet 3100 (Ol' Roy)

1939 Packard Standard Eight Coupe (The Phantom) | 1956 Cadillac Coupe de Ville (The Bismarck) | 1964 Ford Galaxie 500 coupe |1966 Ford Mustang (Little Red) | 1969 Pontiac GTO (The Dishpit) I 1979 Ford F-100 | 1976 Ford F-150 (Big Red) | 1995 Ford F-150 (Newt)