Thank you, thank you and THANK YOU!
My iMessage broke way back in 2014 and even on Mountain Lion, Mavericks or Yosemite, nothing I could do even with Clover (after a major headache upgrading from Chimera), could fix it.
I wasn't so lucky the first time around, however you highlighting the iMessagedebug output brought to my attention that my ROM and MLB number were not consistent upon reboot. Turns out filenvram.kext was still stuck in S/L/E. Once I removed that and rebooted again, I was able to sign back in with no problems.
Migrated my messages from another laptop, and I'm happy as a pig in mud.
So thank you so much!