LOR's is the one area where non-trads are at a definite disadvantage. Most school do not give you the same consideration without a "pre-med' committee letter, as I found out my first round of applying.
I went back 4 years to my old professors, who barely remembered me, but could look up my grades in their classes. One science professor who I needed a letter from had passed away, so it was definitely tough to get them sorted out. I sent them preaddressed/ prestamped envelopes and asked them to drop them in the mail after signing the flap to indicate they mailed them. It worked for 2 schools where I got interviewed - out of 12.
Some schools allow you to have your coworkers/supervisors submit letters, which I did. But frankly, these letters aren't given the same weight as a science professor whose sole job is to grade your scientific abilities in the classroom/laboratory.
The only sure way to go around this is to take classes as a postbacc/or special student and get a committee letter. That's what I did, and I got accepted this round pretty early on.
Do I think the difference was just the LOR's? No, but I think they were a major piece of the puzzle, since most schools base who they invite for interviews solely upon the committee's evaluation - which is why it's so important.
Good luck.