My preference would actually be to create a "GO for the rest of the Province". Call it ONrail or something like that. GO would be for the GTHA (under Metrolinx), ONrail for the rest of the Province (under the MTO). Have the service by a hybrid between Via and GO, and have it run the more local routes that Via refuses to adequately service. In places like Ottawa it could serve a quasi commuter rail function, but in most places it would basically be a milk run Via train that is run by the Province instead of the Feds. Let Via focus on the express Tor-Ott-Mtl passengers, and let ONrail service the communities in between.
In SW Ontario, you could have routes like London-Sarnia, London-Windsor, London-KW, and London-Hamilton (Via would still do Toronto-Windsor with a stop in London). In Eastern Ontario, you would have Ottawa-Kingston (via Brockville), Ottawa-Hawkesbury, and Ottawa-Pembroke (or Petawawa). In Southern Ontario, you'd have Toronto-Kingston (via pretty much every current Via station along the line). And in Northern Ontario, you'd have Toronto-Sudbury via North Bay.