Not to drag this out more than it needed, I had one final observation.
After verifying the tone mode for the Anytone AT-588UV should be set in Chirp as:
"For RX using CTCSS and TX with no CTCSS (or DCS)...
Tone Mode: Cross
Tone: N/A
ToneSql: {required CTCSS tone} Cross Mode: ->Tone "
I opened the OEM software and in the column at the end of the row you can double click on for more advanced settings. Inside there is the Tone Mode setting allowing you to choose between Carrier and CTCSS/DCS. When the settings are as above in Chirp, when the radio is read from the OEM software the Tone Mode is still set to Carrier. I then set the Tone Mode to CTCSS/DCS and wrote back to the radio. So far so good. Just find it odd that I have to set that menu item using the OEM software to set the channel to CTCSS.