I have to say, this whole idea of "cold calling" or otherwise pestering a DO to get a letter is kind of contrary to what the real purpose is. I'm not criticizing you pre-DO's for doing it, I just think it's kind of crazy that it oftentimes ends up like this.
I worked with a couple of DO's in a hospital a few years ago and tried, unsuccessfully, to contact them. I also tried contacting a DO who actually wrote a letter for me the 1st time I applied (1993), but she politely referred me to several DO's in my area to bother.
Ultimately, I never got a letter. I decided that I'm just going to tell them in the interview that I tried the 3 DO's who I actually knew, but couldn't get a letter from any of them. I'm also going to say that I felt it was disingenuous for me to just track down an anonymous DO who I have no relationship with just to get a letter. There's not much else I can do.