I scanned ,but haven't read all of the posts in this thread, but something that I consistently see not mentioned about the old type of starter relay is that they can be opened up and reconditioned. I've like done 30 or 40 of them over the years. It's not complicated. Drill out the 4 corner rivets and clamp the bottom plate in place before you drill the last rivet as the spring in there will send it flying.
With it opened up you have the two stationary contacts and the moving contact. Odds are good that one or all three are a bit eroded from arcing. Usually the stationary contacts can be removed from the solenoid body by removing the second nut. Some designs allow these to be flipped over, and re-installed. Some do not. Either flip them over to get a new contact surface or carefully clean up the contact area with a mill file. The moving contact can sometimes be flipped as well, but most can't be. Same thing, clean it up with a file.
De-grease every thing, clean any copper dust out of the inside, and reassemble. We use short machine screws and nylox to replace the rivets.
If you really want an over the top solenoid/relay with almost the same size and shape then have a look at these:
Note that the 250A rating is continuous, the 30 second rating is 1000A. They are hermetically sealed contactors, and most of them in that family of contactors are rated for a minimum of 10,000 cycles (some are more).
As was mentioned above, these too have no 'I' terminal on them. Running a "Sugar Cube" relay in parallel would be how I would address this issue.