Age old problem with these. I have one, my wife bought it back in 2014 for me but I rarely wear it as the bracelet is crap. Loads of people have the same issue as such little adjustment.
I also added a half link. Back when I did it the only option was a conquest half link which is squared off at one end so it’s not quite right. I see they now gave a proper one which you have.
The 2 issues seem to be because the bracelet doesn’t taper down in size and the clasp has hardly any micro adjustment.
If I were you I would try with the fix you suggest. If it doesn’t work you haven’t lost much. You won’t wear if it’s not comfortable.
If that doesn’t work put it on the rubber strap. Think I will be doing that as soon never wear mine.
James