Tory, I don't wish to contradict your CYA. This sounds like a good idea. However, I personally believe it may be overkill.
I lived in Beverly, MA for six years, during which time I had a Class A LTC. I moved from one part of town to another during this time, and sent the change of address letters. Not that I expected any response, but for the record I did not receive one. Later, I again moved from one part of town to another. This time I did not send change of address letters to either the town PD or the Staties in Chelsea. Some time later, I sent in my renewal application. I got my new Class A LTC without any fuss. So either:
1. Beverly/Staties didn't care about my change of address because it was within the same town, or,
2. I got lucky.
I did not send in a change of address letter when I moved to New Hampshire because I didn't believe it was necessary. Until I can review the law I will again agree with your suggestion. Perhaps I have put the procural of a NR MA LTC at risk by not doing so.