I did my postbac at UW starting nonmatric, then admitted. There's no way I'd do it again. UW is HUGE, crowded, isolating, impersonal, soul-crushing, and you'll kill yourself to stay over a 3.5. Very difficult to get LORs from professors. There's no benefit to a UW postbac when you try to get into UWSOM. If I could do it again, I would have done a structured postbac like Bennington or Mills.
I applied for postbac admitted status after summer '05 as a nonmatric, and got in for winter. At the time, it seemed like everybody I knew who tried this got in. But given the current admissions environment, it's got to be tougher now.
For a nonmatric, genchem and non-calc physics are no problem. You'll probably have to take night labs. For ochem you'll need to take it off-cycle, and you'll probably have to take lectures at night.
Your only chance at bio is during summer, which means 3 summers. No way you're getting in during the school year. There are always at least a dozen regular students trying to get in ahead of you. And if you try, that means you're investing 2 weeks before you find out if you have a seat - 20% of the quarter, gone.
You have no chance at genetics or neurobio. The lower-level biochem is no problem, and upper-level is possible. Any of the biomed major classes require you to wait for all majors to register first.
I suggest that you go to Portland for PSU's program, or maybe do UPS in Tacoma. I don't recommend Seattle U or SPU, but either is better than UW. Or, you can take prereqs at a CC here, and then take a year's worth of upper div science at UW.
Best of luck to you. PM me if you need more info.