@Mame,
I think you misread the contract. I know I'm older and fogier, but I would have asked. Whether or not they pay you isn't the key part, it is whether you with your talents can cover the work that they were hiring for. The medical part is important to the docs, I presume. Again, not that I know what you do.
You are looking to have the anxious one replace you? Or they contract for a temp?
Sorry to switch sides, but I think you are naive on all this.
I've worked in medicine from a lame-o minifilfm xray tech at sixteen, in 1957, to cashiers, to admitting, to reservations, while working as a medical assistant at the same time, to lab trainee after degree, all the while, to lab trainee after hired, to the person who ran a lab, and so on.
The docs will like their place covered.
I'm not clear re your work, but you are sounding spritely.
Again, not knowing, if the docs are ok with a temp all these times, there you go.