Best way is to ask a DO if you can shadow him or her for a few months, or if you need the LOR now, a couple of times this week or over the next couple of weeks.
That way at least you can talk to your DO, and they can get to know you a little before writing the letter.
What I did was check my insurance list of doctors and noted the DO's in the area. Call some of them and see what happens. It is awkward, but it's just one of those things you have to do if you don't already know a DO.