The best option for Toronto - Mississauga connection would be a RER-style service on the Milton line, with an underground diversion to connect directly to Square One.
If CP feels this is a non-starter, and there is no chance to redirect CP freight to the northern bypass, then I would consider building a spur of the Lakeshore West line. It would split off the main line roughly in the Dixie & Lakeshore area, and run in a tunnel, diagonally to the main street greed, until it reaches Square One. Definitely more costly than a Milton line spur, but comparable in cost to Bloor extension, while being much faster for trips to Toronto downtown.
The third option, very theoretical at this point: a branch of the Relief Line West subway, serving the southern Etobicoke and then continuing to Square One. Presumably, the stop spacing would be wider than on the Bloor subway.