Hi man,
I believe that Asterisk is not a good choice for PTT services, however it does support on variety of protocols and include many apps for amazing services, but having ptt on asterisk is a little bit strange.
Anyway, I am here, A talented and intelligent Asterisk Engineer with recognized strength in VAS solutions based on asterisk.
I have also done many asterisk based projects in Mobile Network Operators for their VAS dep.
Please feel free to contact me to discuss about the details.