I just read through the whole thread - phew... But having come to the end of it, I still have in my mind an idea that came up right at the beginning. It must be my background - a Mediterranean attitude to rules that automatically seeks to find the loopholes. So:

Why not simply ask a Jewish family, or even individual, to live in the Shabbos house permanently. There must be a way to assign the house to their name without permanent ownership being lost. Then that becomes a normal residence for someone, who simply chooses to have lots of "friends" come visiting for the weekend.

Or, here's another thought: Sell the house, and with the money ask the hospital if they would allow you to build something on their grounds - some space that will be owned by the hospital (donated by the Orthodox Jewish community, the hospital's to have and to keep) but whose use as a Shabbos dormitory can be stipulated for as long as the Jewish community needs it. In fact, I would have thought that this would have been the first action when the usual dormitories were lost, not the purchase of a house.