If your at all handy cut a wee bit off the old one and face it with a thick piece of leather. Or just make up a new one from silicone and leather. It's just a bumper to cushion the bolt at it's most rear ward position so it doesn't have to be fancy just functional.
Yes I have a SX-1. I was probably one of the first fellas to have one. I shot skeet with a Win rep in the early 70's I had an SX as soon as I could get my hands on one. Have owned several. Still have the original. You may not get your hands on an original bolt cushion which was made of a little softer material than the latter ones. Thus the problems you are experiencing.
I put about 40,000 rds, through my original SX which included alot of stiff hunting loads before I replaced my bolt cushion. And then I really didn't have to I just did it to be proactive in the maintenance of the gun. These are a great shotgun. So far superior to Rem 1100. that you can not really put the two in a long term comparison. These guns were made from machined parts not stamped. Winchester could not make these guns and sell them at a competative price so thats why they eventually went out of production. Of course they cheapened a few things in the latter years like bolt cushions. 3mac's 1 on this site is probably the resident expert on SX-1's if he can't find you a decent bolt cushion your going to have to go my route and make one. He's the expert, I just shoot the dam thing,clean it, shoot it some more etc. etc, and the years keep going by and by.