All certainly possible.
The Contacts and friends in Seattle sort of cut against your thought because if she was getting out of the way because she was in an unfortunate pregnancy, she wouldn't want to be accessible to contacts and friends. Further, if that had happened, they would all have known exactly what happened and yet none of them said anything about it when they were being interviewed when he was running for President.
Don't think a mixed race baby would have had any reception in Canada in 1961.
I don't see what the last paragraph adds to the analysis. She might have enrolled by mail at the U but in the fall of 1961, the U of W was a relatively looser operation.
She didn't stay in Seattle because whoever was paying the bills and calling the shots wanted a record that he was a citizen in Hawaii and thought it was important to get him there.
If I had been in charge of her record, or her mother's effort, I would have got the kid back to Hawaii as soon as possible after birth; called one of my doctor friends who delivered babies at one of the local hospitals; got birth document forms filled out complete with the footprint; and had him slip them into the stack with the rest of his deliveries at the hospital. If she'd done that, we wouldn't be having the discussion even though we know he was born in Mombassa.
Questionable what they did do but I think they took him back to Hawaii because the planned to do something to report his birth that required his presence. Further, I suspect that given the fact that she had been living the last six months with his family in Kenya, they all hoped that she would just move back in with him and establish a happy little family while he was in college at U of H.
The decision to send her to the U of W was made in later August after it appeared that dreamworld wasn't going to happen.
It takes time to enroll in a new school, especially one outside your state of residence, more so in 1961 than today. You have to apply for admission, get accepted, etc, etc.
Even in state, I had to start the process in the winter of '67-'68 to enroll in fall of '68. I doubt U Wa was any more efficient, than U. Nebraska. I know Oklahoma was still less efficient than Nebraska had been in '67-68 , 7+ years later. Although enrolling as special, non degree seeking, grad student was easier than undergrad or regular grad student. She didn't stay in Seattle because whoever was paying the bills and calling the shots wanted a record that he was a citizen in Hawaii and thought it was important to get him there.
Washington state, or any other state would have served just as well for making him a US Citizen, which would have been the objective of any scheme to show him born in the US, rather than someplace outside the county. In '61 even commies thought being a US citizen was a worthwhile thing. It was just easier to "fake it" in Hawaii, for several reasons, one being Grandma Toot's position in the area.
Most likely she didn't stay in Seattle because, BHO Sr, was no longer in Hawaii, she had money troubles, and probably Grandma and Grandpa Dunham were re-thinking the notion of being isolated from their grand-baby and daughter. Time heals those sort of wounds. I know it finally did for my wife's family when her sister married a man of a another race, and had two children with him. Believe me, not only is he the best of her three husbands, he's a hell of a nice guy, unlike BHO Sr, who was a womanizing drunk.
The agreement to give up the baby was more likely something Toot came up with. Stanley Ann could go to Washington, which is what she wanted anyway, in exchange for going elsewhere to have the baby and giving it up for adoption. Under this theory, the friends in the area, Toot's friends, would have helped locate a place where she could have the baby and which specialized in "unwed mothers", even if S.A. wasn't unwed, and finding homes for the babies. There is just such a place "Grace Hospital" in Vancouver. The friends may possibly even have provided a place for Stanley Ann to live for the last months of her pregnancy.
Even though classes at U Washington didn't start until late September, one would need to show up a few weeks early to find lodging, probably go through class registration, and otherwise settle in, before classes started.
Questionable what they did do but I think they took him back to Hawaii because the planned to do something to report his birth that required his presence
The official Hawaii birth certificates of that era did not show footprints, or anything else that would positively ID a person as being the one described on the certificate. Normally they had the hospital and doctor's name (and signature) but even that wasn't required if the birth was reported as being "at home". All that was required was a signature of a witness in addition to a parent's signature, (usually the mother's). You did not even actually need to prove there *was* a baby at all. You could create a false person, if one had some reason to do that. However the BC would clearly indicate a "home birth" and that alone would be somewhat suspicious given the 'station' of Stanley Ann's parents, particularly her mother. Something a "native woman" or a "farm worker" might do, but not the child of a banker. It wasn't cool in '61.