We are using conf bridge capabilities and AGI/AMI for manageable teleconference program with Web UI . Its persian but you can get the idea . conference manager can mute/unmute/kick/hangup one or all participants .
As you said, combination of AGI and AMI can achieve the use case. I tried and can see asterisk manager events for DTMF presses and Conference application.
I was trying to omit the use of AMI but it seems it cannot be done by AGI alone.