Eureka! I believe I have found the solution!
I was under the impression that
all state public medical schools were not only located within the state's largest city (or cities), but were also affiliated with the
University of [State] system of higher education; the former for obvious reasons of access and the latter for reasons of maximizing prestige. Generally, this is indeed found to be the case.
But I have found an exception to this rule that works well for Oregon: The Ohio State University College of Medicine. In other words, the OSU College of Medicine!
The ramifications for an Oregon State University College of Medicine work beautifully:
(1) Portland State is officially renamed "Oregon State University at Portland" (OSU-Portland) while still popularly being referred to as "Portland State." We see such usage in examples from the California State System (e.g. "California State University at San Diego" being popularly referred to as "San Diego State". This gives PSU (or OSU-Portland) political jurisdiction at the level of the
entire state (and not just the metro region). In other words, the entire state's reputation is on the line and they are compelled to make the university as good as they can. This gives it the political punch it needs: PSU's official name gains a quantum leap in terms of prestige while retaining its affectionate, long-held name. Another step up in PSU's evolution with accommodation for OIT on the Portland campus.
(2) OSU is much more humble-minded and thus merit-based than the UO. The UO tends strongly toward elitism while OSU tends more toward producing true value. The UO needs its requisite infusion of wealth to become a truly nationally- (and internationally-) recognized elite university (along the lines of Stanford, USC and Penn). OSU adds tremendous value to the state through its influence which is then spread to all of Oregon's university towns: Portland, Ashland, Monmouth, Klamath Falls, Lagrande and, of course, Bend. The entire system can then be renamed the "Oregon State University System," that is, so long as the UO is given something of at least equally strong political value to compensate as OSU-Corvallis becomes the flagship of the state system.
(3) That something is enhanced bond-writing authority from the state to help the UO become the elite private university it has always desired to be, but with a state covenant in place
a priori to allow access for deserving Oregon students. Instead of the UO tapping nearly
all the state's debt-writing capacity for higher education (as they recently tried to do), we allow them a full third of capacity in order to catalyze upward their elite status. The rest of the financial strategy has to come from UO alum millionaires, billionaire, practitioners, administrators and strategists. This is the UO's chance of a lifetime to gather together their best and brightest and make their alma mater university as good as they can. The sales price of the UO campus is about $11B paid to the state according to moderate interest installments over the course and life of the UO state-sponsored bonds issued (traditionally 30 years).
(4) The result is the UO becomes an internationally-recognized, self-supporting, elite private school (providing covenant access to deserving Oregon students), OSU's meritocratic culture is applied to all state university campuses from which tremendous value ensues. Portland State & OHSU become OSU-Portland (a.k.a. Portland State and OSU College of Medicine respectively) with a quantum leap boost in prestige for PSU and a worthy university home for OHSU ([OH]SU = OSU). The team name is still the Vikings with school colors either retained or influenced by OHSU). Go Vikings!