You may have a mismatched starter and ring gear. Things get changed over the years by prior owners and it's not always correct. Frankly I always have trouble keeping it straight,so verify with the catalog before ordering. I think the early ring gear was shrink on and the later was bolt on. It must be matched with either the bull nose starter(early) or open starter(later post 50,000 vin), as your photo, which is for the later or bolt on ring gear. If not correctly matched it will cause the issue you mention. I bought the modern gear reduction starter and like it very well, but not original if you're a stickler for original. I just bought the basic reproduction clutch parts out of the catalog which are fine for normal driving. From your photos, I don't understand the chewed up edge on the clutch??? So, 1) verify the engine number is close to you VIN, to determine someone has not put an early engine in your car, 2) verify that the ring gear is bolt on which would be the correct part for late engine. 3) decide if you want a newer more efficient starter or get yours rebuilt. 4) decide on OE or heavier duty clutch...then your set. I've got a '61 that had a '58 engine in it. now has a '67 TR4 engine with a '58 application starter and fly wheel. Fly wheel and starter will work on either as long as the two are matched.
ps: I have a later fly wheel with a good ring gear if you need one. It's off the engine I bought to replace the '58 cracked block. I would have used it but already had bought the early starter.