I enabled Automatic Breakpoints > Before Requests but there are some arbitrary background URLs I'm just not interested in stopping, like for example after I enabled it there were like 8 requests to http://detectportal.firefox.com/success.txt. I would have preferred to select all those sessions and then 'Run to completion' for all of them in one fell swoop but there doesn't seem to be a way to do that. Instead it seems I can only initiate an action per session. There is 'Abort Session' but that just causes the browser to retry the requests which creates more sessions.
v4.6.20173.38786
Built: Friday, September 15, 2017
Thanks Eric, that works.
(To revise my response: g in QuickExec unpauses ALL sessions in the Web Sessions list, as does the Go button. Shift+Go unpauses only selected sessions).
Select all of the sessions. Press g in QuickExec or click the Go button on the toolbar.