@scottalanmiller So since I posted the OP, I found out what the issue was. (or at least eliminated it by changing a setting.) On old versions of FreePBX, in Advanced SIP settings, in order to enable TCP connections, you had to manually type:
tcpenable =yes
In new versions, there is now a button to enable TCP. Having both settings enabled seems to cause these issues. Most likely, the config file for sip.conf gets messed up having these similar/identical settings. Removing the old entry eliminates the errors.