So, we lived in mexico from 2004 to 2015 but in order to have US bank accounts you need to establish a US address. There are a number of (or there were) businesses dedicated to this and the most popular are in SD and TX (due to lack of state taxes there). I have no idea of the RN licensing requirements WRT state residency so you might have to check your current state to see if that will carry. Additionally, as others have said, the travel company will likely have good info on state requirements.
FWIW, when we lived in MX there was a lady who worked 3 mo at her home hospital, flew to MX and stayed there for a month or so (not sure how long). Not sure if that would be a possibility. She worked in the ER in her hospital.
Sounds like a great "retirement".
Also, where in MX are you thinking? (just curious)
Oh, and it takes a while to become a permanent resident of MX. MY son, husband and daughter have it but I and my other daughter and other son do not. Weird. I would suggest temporary residency for a while (you will likely only qualifiy for permanent after 4 years of temporary anyway) as it gives you some protections that permanent does not. Course things change there, so that may be moot assivice.