I don’t know when they changed ... but S1 and I’m assuming early S2 had BSF studs that were threaded at both ends, and peened over on the back to lock them in.
Later these were changed to the splined shoulder type you describe, which were meant for a larger hole and to be pressed through from the back. (i.e not screwed in)
It sounds like you have the first type of hole and the later type of stud.
Now you can get the original type of stud and you could (in order of correctness/bodge) find a way to pean/press them over on the back edge, or chemically bond them in, or (horror) put a blob of weld on them.
The other option is to drill them out, countersink the back so it sits flush and comes through enough, and then press them in.
I have just replaced 2 on my series one... 1 had been pushed through and welded, badly. It was absurdly short. Another was one that had been drilled out and pressed in - but it was now seized and hadn’t been countersunk and as a result was short on the face.
So I replaced both with the later type countersunk - primarily because both holes had been enlarged with no opportunity to put in the original types.
I got an engineer to do it - with them having been bodged I didn’t feel I had much leeway to get it right, and my old puller drill and an angle grinder didn’t seem Like the safest approach.
Happy to take some photos of that would help.