These rims are not "safety Beads" so they break down much more easily.
Most times I can put both heals on them and a tire bar between my heals and
one hit with the #8 sledge and it is broken down, sometimes just my heals are all that is needed.
You can cut a liner patch from a old inner tube or another worn thin tire, but stay away from radials as they have wire in them.
I still have a liner or 2 around here from the 2nd world war days, that they put in tires because you could not buy tires during the war.
It is not cost effective for you, but M.e. Miller has or did have, large liners /patches/ boots for tires.
I did and still do all my tire work and used to run into some old stuff from those days while restoring the old farm tractors/equipment.
You just never know what you will find in a 50-70 year old tire/rim.