The problem with radial railways in North America is indeed the automobile, namely the building of better highways in the 1930s and onward and (the real nail-driver) the development and building of expressways in the post-war era. Even in Ontario, the radial railways proposed by Sir Adam Beck would be badly dented by the building of the provincial highways in the 1930s and killed dead by the building of the 400-Series Highways (especially the 400, 401, 402 and 403). The simple reality is that saving radials and building highways is fundamentally incompatible - as soon as the highways are being built, the radials are gonna wither on the vine no matter what you do, particularly with distances in North America.
The best bet for such lines to remain operational is for them to be limited as lines between major destinations and built as passenger-carrying lines meant for longer-distance travel purposes. If you're starting from Toronto, you would be effectively creating a genesis for GO Transit (which began operations in 1967 IOTL) in the 1920s. Having a Government of Ontario Transportation System based on Beck's proposed radial railway line ideas but acting similarly to modern commuter rail has possibilities, but even then you'd have to limit the scope, and population densities would be an issue in many routes.
Starting similarly to GO Transit's busiest routes (Lakeshore West and East and the Kitchener line) would make sense in the 1920s as there would be plenty of population there to provide a market. Going from Toronto east to Oshawa, west to Kitchener-Waterloo (via Guelph) and southwest to Hamilton, and then eventually along the south side of Lake Ontario from Hamilton to Niagara Falls via St. Catharines, would be good territory for a radial railway. Creating an oval-shaped route by extending both western lines to London (Kitchener to London via Stratford and Hamilton to London via Brantford and Woodstock) would be feasible, as would extending north from Toronto to Barrie via Aurora and Newmarket. (Highway 400 might do in the Barrie line in the 1950s, but if you extend it to Orillia or maybe even Gravenhurst or Huntsville might give it a new lease on life once the cottage country boom begins in the 1950s.)
If anything, Ottawa might actually provide better opportunities, as you could easily run from Ottawa to Montreal via Rockland, Hawkesbury and Blaineville, as well as south to Kingston (via Smiths Falls) and northwest to Petawawa (via Pembroke, Renfrew and Armprior). If the funding (and market) exists, Kingston to Montreal (via Gananoque, Brockville and Cornwall) may be feasible too.