When I had to move cross-country, I pre-wrote a little letter just detailing that my rent was paid on time, no noise complaints, my animals were behaved, etc. I showed it to my (then) landlord asking if she would sign off on it, just as a reference for a new place. She was more than happy to and it saved her from having to write anything.
Good luck! I hate moving and hate interacting with new people even more. kek