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Yes! Many old banjos were comprised of all handmade parts, nuts, bolts, shoes, screws all individually made! When the banjo was first assembled some of the shoes were probably slightly thicker than others so the screws from the inside made slightly longer. Others a bit thinner so the screws made shorter. At some time in its life it may have been disassembled and the parts mixed up on reassembly. This can result in some longer screws going right though the "thinner" shoes and clamping on to the tension hook! The shorter screws fitted in thicker shoes hold OK, but don't screw in as far as they should.
I suggest trial and error re-assembly checking screw lengths until you get the mix right and the tension hooks are not gripped by the screws... good luck!
Yah, like Ian sez, old banjos can be a complete mix-up of parts. I have found that, generally speaking, banjos such as yours have had the screws tightened down many times over the years and the wood underneath has simply squashed down allowing the threads to run too deep thru the bracket. Very common with lower grade banjos as the wood was poor grade to begin with.
My solution for my "Monarch" (made by Stratton) is to get rid of the screws altogether. I purchased threaded rod of the appropriate size and cut small sections of rod (appropriately sized). I screwed the rods into each bracket with Loctite (the red stuff) adhesive, making sure the threads don't impinge on the hook-hole. Then the assembly is no longer with screws but nuts. I bought shiny nickel acorn nuts for the Monarch (another unfinished project) but decorative brass nuts can be had from lamp suppliers, etc.