Forgive me, but I would expect the TiVo to go missing from the nursing home room at some point down the line. Nevertheless, I would love to hear who you resolved this. I guess the question is if the nursing home is re-modulating using NTSC or QAM. QAM would be more likely, but if it is an old system, I would not be suprised if it is NTSC. But the TiVo should be receiving both at the same time if you choose Analog, IIRC, but it is something to be aware of when testing, so test every channel.
The other problem would be getting the EPG data because as of recent change, TiVo no longer uses telephone numbers (POTS Copper), but rather Internet only to distribute (and otherwise contact for functionality) EPG data and necessary software--espescially post Rovi for EPG data--and other updates. You can use WiFi connected to the wired gateway, and I believe TiVo has the speicific details on how to acheive this with the proper hardwar choice, along with others who may chime in.