Your question - is the stud too small...
I assembled and disassembled two Gillette Techs, which also use the 10-32 thread, using both the Rockwell and the two original aluminium Tech handles. Using the Tech heads, all three handles were loose with quite a lot of play, but tightened correctly and held OK. Using the Rockwell top cap and stud, the Tech handles had less play than with their own Tech top caps. So this suggests the 6C stud isn't undersize. When I fitted the 6C handle on the 6C head the play was horrendous - the handle hardly engaged with the stud. So my observation is that it's the handle that's the issue. Anyone who has a Tech in their collection can try this and see if they get the same result.
In a world of M5 threads I've no idea why Rockwell used the 10-32 thread, or even if the Chinese factory making the parts is using M5 or 10-32 or possibly mixing the two. I haven't tried screwing up the Rockwell handle on a M5 head because that might damage it even more. I carefully and very lightly started the Rockwell handle on a M5 top cap and it stopped part of the way, and I removed it at that point without using any pressure whatsoever. So I believe the handle is a 10-32 thread in theory, though in practice the tooling used must be worn or out of tolerance because the threads are very sloppy indeed.
So my conclusion is that the stud on the top cap is less of an issue than the thread in the handle, which points to trying out other handles. Since almost all handles use the M5 thread, they're going to be looser anyway. Whether the stud will hold up over time is anybody's guess.
I assembled and disassembled two Gillette Techs, which also use the 10-32 thread, using both the Rockwell and the two original aluminium Tech handles. Using the Tech heads, all three handles were loose with quite a lot of play, but tightened correctly and held OK. Using the Rockwell top cap and stud, the Tech handles had less play than with their own Tech top caps. So this suggests the 6C stud isn't undersize. When I fitted the 6C handle on the 6C head the play was horrendous - the handle hardly engaged with the stud. So my observation is that it's the handle that's the issue. Anyone who has a Tech in their collection can try this and see if they get the same result.
In a world of M5 threads I've no idea why Rockwell used the 10-32 thread, or even if the Chinese factory making the parts is using M5 or 10-32 or possibly mixing the two. I haven't tried screwing up the Rockwell handle on a M5 head because that might damage it even more. I carefully and very lightly started the Rockwell handle on a M5 top cap and it stopped part of the way, and I removed it at that point without using any pressure whatsoever. So I believe the handle is a 10-32 thread in theory, though in practice the tooling used must be worn or out of tolerance because the threads are very sloppy indeed.
So my conclusion is that the stud on the top cap is less of an issue than the thread in the handle, which points to trying out other handles. Since almost all handles use the M5 thread, they're going to be looser anyway. Whether the stud will hold up over time is anybody's guess.