UPDATE: for those in the same position, I can confirm that your landlord / Condo management does have to register a new TM30 in Chiang Mai.
Is Chiang Mai immigration one of the places that are strict on registering a new TM30 when you leave and re enter the country? I have to spend a few days outside Thailand to get my non B visa, and past posts on this group indicate that this requirement can vary depending on location.