Howdy,
I can't help you directly but perhaps the clinic can: I'm sure they have this issue to respond to on a regular basis.
I do know one very nice rehab clinic on the lake of Constance - Klinik Schloss Mammern
http://www.klinik-schloss-mammern.ch/ - which is utterly magnificent, although around 45 mins away. They offer full service rehab and guest accomodation in beautiful lakeside surroundings.
Perhaps you could search for 'Apparthotels' in Zurich, there're are plenty of them with full service facilities, although you'll pay a fair whack for this. There's a large one at the hotel Intercontinental. Considering the short duration stay against residential stay, maybe a hotel would work out just as affordable? Send a few e-mails and see what they can offer - and tell them your story too. Good luck!