Good question. Per OP:
…so whomever is looking at that info could be considered some level of “admin viewer”. Maybe “ops viewer” is better term…
Good point. Audio streams are not exactly part of OP – although the second half of the title “/ Live Calls Monitoring” was a little muddling. Unless there is need to patch in the audio eg. ChanSpy() style, then WEBRTC soft phone is probably too much stuff.
Besides AMI, another extremely loosely coupled approach is with CEL into database backend, which can provide all but one of the OP’s requested columns (the exception being Duration which can be calculated on-the-fly from the most recent CEL record on the call.)
Also a PRO for CEL would be the ability to add a “temporal rewind” feature – probably more easily than AMI – to let the “ops viewer” look at what the Active Calls were at some point in the past.