Two Timin'

Build a professional portfolio. That makes it easy to add a new agency, just ship them all your documents - after being careful that you truly want to work for them. Three to five agencies is about the max you can handle.

A professional portfolio includes written references. That allows you to be very selective and reduces, often eliminates or at least shortens dramatically, annoying calls to your references. At some point, your references will no longer be located at their prior place of work, but your references will still work since your referee can be verified as having worked there. I often discover that an old one really performs when a manager at a new hospital had previously worked with that referee.

I also collect written references on every assignment and you are perfectly placed to start your collection from the beginning of your travels. I collect them early and often, going as high up the food chain as I can. I go for charge nurses, managers, and directors, but your peers in a pinch. I have one ED friend who loves to collect them from physicians. Collecting them early (I start at week 2) also serves as protection from a false claim of incompetence, false termination, and even a personal emergency when you have to quit before your contract is over. It is very difficult to get references after you have left a facility, and most have personnel rules not allowing it.

Yes, agencies will also collect written references, but they are not going to share them with you. Too valuable, and makes it easy to, guess what? Sign up with another agency.

PanTravelers has a couple of travel specific blank written references that can even be customized. Under downloads after you have signed up for a free membership.

Personally, I hand one over and stay right there until they finish it - about three minutes (do what you like, but promises to complete them are often broken). That allows me to tell them this is a reference for external use, not a performance eval for your personnel file. I also encourage them to write at least one sentence of narrative, not just check the boxes. Even as little as "shows up on time" is very powerful, and something the interviewing manager at your next assignment will love.