Webrtc clients are expected to live in web browsers and JavaScript libraries that implement the clients are expected to be run there.
Therefore I am looking for hints, shims, hacks, or clever programming where Asterisk can act as a webrtc client by implementing some service’s JavaScript API.
Hi fellow Bill 
Interesting … to what end?
“the other” Bill
Examples…
Asterisk to join an Amazon Chime meeting with video.
Or a Twilio video room meeting.
There are other video services that publish webrtc JS APIs.
Once Asterisk is joined, you have the full suite of Asterisk abilities to do things like bridging SIP phones or PSTN gateways, execute dialplan, etc…
Asterisk has a websocket client, but it’s currently not really be used so you’d have to write something around it.
Some tests were written around so you can see an example here.
Lastly, for another example usage, and because you specifically asked for javascript type implementation (assuming socket io here), you can take a look at the res_socket_io.c and res_socket_io_websocket.c under the chan_respoke project.
Again the interface currently isn’t really used, so your mileage may vary.
Interesting leads; thank you. I expected to be working from PJSIP with a sort of PJSIP → jssip → webrtc kind of pipeline, and this is a totally different approach.
The webrtc realm is sort of build i yourself.
One option is if you are a queuemetrics shop to use there webrtc client. But its all a bunch of hard choices.
Indeed. SIP has its ugly moments but at least it is intended for interoperability.