Some questions about cooling a two floor apartment

I'm trying to figure out how to cool a very hot, poorly insulated upstairs/downstairs apartment, and have a family member with a serious health problem, for whom hot weather is life-threatening. Can't afford to move. Two separate problems:

First question, about upstairs: Upstairs bedrooms are approx. 100 square ft. with large SW facing windows, and get insanely hot. We must be able to cool at least one down to ~65F on 100F+ degree days. We currently have a highly-rated, dual-hose, 12,000 btu Whynter portable in there which cools well if temps are in the eighties, but is totally inadequate for heat waves that are 94-109F. Whynter's rep told me that portables of any brand can only cool to about 20 degrees below the outside temperature (which is about what our portable will do). That means it's 85 degrees up there with it running full blast on our hottest days, which doesn't cut it.

So, my question for this is about what happens if I go too high in btus on the window unit; I'm looking at vertical window units, and have read that portables are about 50% as efficient as window units, which would mean that 6,000 btus wouldn't be adequate, based on what we're experiencing with the 12,000 btu portable. If I get 10,000 or 12,000, what's the worst case scenario if it's too much for the small space? Someone told me the unit would keep shutting off and going to fan, making the room feel humid and warm. Ideally, I'd love to be able to leave the door ajar and cool the hallway and bath upstairs, as well, if that's possible, but the priority is the one bedroom.

Second question for downstairs: The best i can measure says it's about 810 sq ft., give or take, not including the stairs. I'm thinking of getting a 18,500-24,000 btu window unit, and using a fan to move the cool air up the hot stairwell. Someone with quite a bit of experience in home repair told me he thought a downstairs unit would just force heat upstairs and make the upstairs situation worse. I'm wondering if anyone with experience using two window units for a two-floor place can tell me if that's true, and also if the stairway space would create a problem with cooling.

Thank you in advance to anyone who can offer some tips.

submitted by /u/Last_Nerve
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