Jonathan,
Your largest hitch pin can be made oval at its base by crushing it in a robust bench vice. It can then be driven into the plate such that its now-broad dimension runs fore/aft, in the direction of the string pull.
If this is still too loose, I have lined enlarged holes in plates with .005"- or .010"- thick brass sheet stock. This shim sheet does not need to line the entire diameter of the hole. Make it of a large enough dimension to eliminate the slop with whatever hitch pin you are utilizing. Let the shim run wild either on top of the plate or below, and then slice the unattractive waste off with an Exacto knife. No one will ever know it's there.
David G. Hughes, RPT
Baltimore Chapter PTG
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David Hughes RPT
Vintage Case Parts
Glyndon MD
(443) 522-2201
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