Hi alan,
Not sure how applicable my situation is to yours but here goes. I'm updating my original/initial, 2-year license to the 5-year license. I also want to add a motorcycle endorsement to the existing license. Went to the Land Transport Office with my wife and was told I needed a doc from Immigration, verifying my address/location. This was due to the fact that when I first got that 2-year license, we were still renting and I used my mother in-law's address, way out near Krasang. (We now live in town.)
So off we went to the Immigration office at Thunder Castle (behind the KFC) to get two copies of a letter from them. It wasn't too crowded but because we got there about 2 pm we had to wait a bit and then were told to go have a coffee and come back in about 10 min. (total time about 40 min.). Total cost from Immigration for these two copies was about 700 baht, including an extra charge for taking and printing a passport size photo. (I have a bunch at home but didn't think to bring them with me, so now I have another 4-5 extra.) Of course, I had my passport with all the immigration stamps in it too.
So my guess would be, got to immigration and ask for these "change of address docs" (whatever they are) explaining what you need them for. Bring your existing license (and car reg.) as well as your passport and some passport photos (required for this change of address doc).
Hope that helps. Good luck.