Crawl Space Insulation in Montreal
I would insulate the outside walls with the rigid foam board insulation like you described first, but do not do the floor at this point in time. Then see what kind of improvement that provides.

I'm not sure what I would do about the existing vapor barrier that's on the walls.  If you leave it in place and put the foam board on top of it, then it's possible that the moisture in the air in the crawl space will permeate through the foam board and condense on the vapor barrier that's against the cold, outside wall.  So you might want to consider putting the foam board behind the vapor barrier, right against the wall, then the vapor barrier.

When insulating walls to crawlspace and/or basement, I have not found a definitive answer as to where a vapor barrier should go.  I have even read some recommendations as to not use a vapor barrier at all; use foam board insulation that has some amount of permeability and just let the wall breath.

I would like to hear from others what their thought are and experiences have been.