I wouldn't focus on just one program, such as Yale. You're correct in that you should apply broadly and you might as well throw in an app to Yale if you desire. I personally did not have any luck with landing one there as a DO student but did get accepted for an anesthesia rotation at Yale through VSAS which I ended up cancelling since I didn't want to roll the dice and spend a month up there and potentially walk away without an interview opportunity. If there is only 1 DO in the entire program and it is a large program, probably not a great shot as that person could have had connections or absurdly high stats.
If you are doing aways for anesthesia, ask around to find out if they offer interviews for visiting students. I think most do but I got burned by a program that I did an away at and they only had maybe 3-4 DOs out of about 70 total residents so I felt like that was a month where I could have gone elsewhere for that month instead.
Good luck!
