I use to ride motorcyles and carry pager. Clipped it to the top of my shirt, just under my chin. Could hear or feel it well even running down the road at 65 mph. The original cell phones (bag phones) had 3 watts and much more range than any current cell ph. Similar concept to the 3 watt repeater someone mentioned earlier. I would give the repeater or 3 watt booster a try if needed.
Most hopitals will spend the $ to find any reasonable solution for your situation. I do think you should be compensated for being on call 24/7. I do that for my employees, who are not as skilled as you are at your job. However, if you are paid to be on call, then you are expected to respond or be able to respond IMHO. If you are compensated to be on call and can't respond, you may lose your job.
Hospital should have a back up plan if you cannot respond (vacation, illness, personal emergency ect.) Your job seems like mechanical repair or engineer? Other companies can fulfill that need in emergent situations. It does not alway have to be you and redundancy needs to be considered. I work in the medical field. Hospitals hate not being able to perform in critical situations. You will never win any hospital battle if it goes against patient care or critical situations. Not having OR capability or providing expected critical services is one of those. You and your boss will need to find a solution. It will occur again in the future as it has in the past. Maybe next month, next year or in five years. The problem this time seem minor. A compressor issue. However, no one knew how critical the situation really was at the time. Can't risk doing a surgery if a known potential malfunction could occur. Cancelling or diverting OR time is major issue for a hospital.