The only formal postbac with linkage on the west coast is Scripps.
You won't lose your WA residency by going to school out of state.
OHSU and UW aren't going to have a preference on formal postbacs.
You don't have better odds at OHSU by being from WA. But OHSU has less instate preference than most public schools.
Pick a postbac where you'll thrive, where you'll get A's, where you'll have lots of faculty interaction, lots of opportunities to get into labs and such. Put some thought into what it will cost you, and how you'll handle debt during med school, but finance is only one factor. These things don't matter very much: getting done in a year, avoiding a gap year, getting the MCAT done on schedule. Focus on quality.
If there's a benefit for you in staying close to home before med school, I suggest looking at a smaller school, maybe a private school, that has really strong academics without the slaughterhouse feel of UW. UPS, St. Martin's, Gonzaga, etc. Portland State has good structure.
I did my prereqs at UW and I regret it. I would have gone to Bennington if I could do it again.
UW and OHSU are very different schools. UW has a mandate to serve WWAMI, 27% of the US land mass. OHSU serves Oregon. If you get into UW, you could be in Spokane for M1-M3. Be a smart consumer.
Best of luck to you.