A stator test is very simple:
Leave key OFF;
Disconnect the Stator Connector (Grey One) from the R/R;
set your meter to read resistance; (touch probes together - reading should change from 1999 or similar to 0.00 - this shows you have correct setting)
Measure between ANY ONE of the three terminals in the connector going back to the stator to any engine ground point with the other probe;
you should get the same reading leads unconnected to anything - if you get 0.00 then you have short and stator is toast.
Incidentally stator cannot 'burn up an R/R' (although the converse could potentially be true)
You say just shut down completely - when you turned key back on was there anything??? Speedo sweep, lights on, clicking etc?
With a generating system problem, although bike may die, it would be unusual for battery to be COMPLETELY discharged so you would get no indication of life at all
You may well have an ignition switch problem - much less frequent (rare but not unheard of) than the Classics
Difference v classics however is on Classic switch itself fails - on Touring failure more typical on the connector.
So unplug the key-switch connector and inspect the terminals on both male & female sides for any sign of burning/arcing.