Little follow-up.
I called them on Feb 11, and they said they never got the copy of my Texas permit from the DMV. They told me to mail a copy of it, along with my TN driver's license, to their office. I did that the next day (Feb 12).
On March 9, I called them again asking about status. They said they were still waiting on my handgun safety course certificate. i told them i don't need to take it, as I moved from Texas and have a valid Texas permit, and that I mailed them a copy of that on Feb 12. They stated they never received it. I asked if I can email them a copy of it and they said they aren't able to do email (in 2015???), but I can fax it. So, I faxed them a copy of my Texas permit and my Tennessee driver's license.
I just got off the phone with them this morning to check the status, and the lady I talked to said my file shows that my permit was approved on Dec 1, 2014, but hasn't been issued. She is going to talk to a supervisor about it now. It's certainly outside of the 90 day statutory limit at this point.