Both of the Providence programs, and the Legacy IM program, have a relatively large number of DOs in them, and I suspect (I work with the Legacy residents and know the program leadership, can't actually comment on Providence) that you're reasonably competitive there. They do tend to have a large proportion of those DO grads from western programs, but I suspect that's a self selection issue.
OHSU is also fairly DO friendly. When I was a resident there, 10-20% of each class was DO, usually from the older programs (CCOM, PCOM, KCOM, NYCOM, etc) but more recent classes have had broader DO representation (Western and Touro in particular).
Bottom line, all 4 of the Portland programs are worth an app if you really want to come here for residency.