I don't think that makes too much sense since to write a LOI - it isn't like Dental school, where you could interview and get acceptances at multiple programs. That isn't the case for ortho match or non-match. I believe all of the non-match programs require you to withdraw from match if you get accepted, so I personally wouldn't, just because you are really only supposed to get 1 acceptance for ortho. Seems like overkill compared to being on a waitlist for a dental school program.
I applied to 40 programs last year, both match and non match. Got 2 interviews 1 for each match and non match. Got accepted into both. You need Just 1.
If you feel like you need to boost your application in every single way possible then I'd say generally a GPR might look more favorable to program directors then working, but by how much? I'm not sure.
I think working also boosts your application too, as you build clinical and pt management skills.
So I'd say it just depends on your situation.. are you able to move somewhere easily for a gpr? do you want to get paid 2-3x less than if you just worked? if there's an ortho program you really want to get into try and do a gpr at that school.
For me.. I have a spouse and kids, and crippling loan debt, so it made more sense to work instead of a gpr. thankfully I felt like my application was decently strong (I think) that I wasn't too worried about it. I increased my shadowing, including visiting a few ortho programs and meeting the directors, volunteering a bit more, reading more ortho articles and textbooks, and boosted my application that way.
and thankfully I got into a program this cycle after not matching last year