i have a micro seiko 1500 where the belt is similar to what you're describing. for years i have used dental floss. use a reef knot to tie it ( left over right and under, then right over left and under) this will never slip. in order to tidy the loose ends. i put a drop of loc-tite adhesive on the knot. let it cure and then you can trim the loose ends flush with the knot. it's worked for me for years now. hope it works for you. it won't cost anything to try it!
.....don
.....don