Batboard

Is there a way in the trunking system mode to not have the radio do the audible "beep beep beep" ID when the public safety mic is keyed?

Yes. Disable the talk permit tone in trunked personalities via the RSS.

I do not recommend that you do it because the entire purpose of that tone is to let you know when the system has secured a channel for you to use and you can use it now.
Disable it, and you may end up talking when the system isn't ready for you yet.

Elroy

In our systems, we have left this beep on but turned it down in volume via RSS. Seems that the MIC goes live before that last beep (of 3) in the go-ahead tones, which is heard as a "knock" over the air.