Many chin straps do not stop your mouth from opening slightly, still allowing pressure to escape. Yet, for many they do seem to work.
What works for one doesn't necessarily work for another as each of our facial features are unique.
I have not personally used a chin strap, but have taped a few times to see if it made a difference in my numbers.
Hopefully someone with more experience with chin straps can help you out.
Best I've found yet--
An "improved Respironics Premium strap design", less bulky, chincup fits snug, says it's made in USA too ! :~) Tighten with mouth closed as much as you can stand it.
I understand your frustration with finding a chin strap that really works. I have tried over a half dozen different straps before I ended up creating my own (Ultimate Chin Strap). Although it is not as "slim" as other chin straps on the market, it truely does work to prevent air leaking and dry mouth without having to tighten it down so much that it puts a lot of pressure on your lower jaw. Below is a link to my video that talks more about the chin strap. I hope this helps.