I love the map by the Bank Street group - it shows a great future network.
I think the Carling-Rideau portion is a greater need, and ought to proceed first. It would include a stint on Bank and so could have infill downtown stations along Bank at Somerset and Catherine, possibly even one in the Glebe before turning west.
As a savings (at least on a relative basis - this line would be expensive), I am not convinced the entire Carling-Rideau line would need to be tunneled. It would obviously need to be buried (possibly cut and cover) along whatever alignment cuts through the west part of the Glebe from Carling to Bank Street, as well as along Bank Street downtown. It should not share the existing Confederation Line tunnel downtown, but could turn east along Wellington and emerge prior to the canal. There is enough roadway for it to cross along Sapper's bridge, and to interchange with Rideau station with this line being on the surface. I am agnostic about whether it ought to enter a new tunnel for the balance of Rideau Street or if it could function in a protected right of way. with Rideau reduced to a single traffic lane in either direction. If it does go back underground, it ought to emerge to be a surface route along Montreal Road and Blair.
Similarly, most of Carling could be a surface route. Certainly through the experimental farm it could have a protected alignment just south of Carling. There may be some tight points where it ought to be buried west of that, but could emerge as a right of way probably west of Churchill.
Growing up in the south end, I always dreamed of a Bank Street subway, initially along the exact stretch proposed (Billings to Wellington), and then possibly extended along Bank further south. I do think that given the existing plans for Line 2, as well as the existing southeast transitway, it just is not a priority as there are other, albeit significantly longer, ways to get downtown from Billings. Basically, the potential cost likely outweighs the benefit for the near or medium term.