I'm guessing from what you describe that you've got about 6 shaves or so on the blade you are using. For me at least, that's about time that the edge on a typical DE blade starts to get rather sketchy and begins to pull. So for starters I wouldn't go much beyond five or six shaves with a blade. So point 1: Change your blade.

A sub-issue of dull blades is sometimes excess pressure. I've caught myself doing this (especially if I'm trying to squeeze just one more shave out of that blade.) It's almost an unconscious response, you think you can compensate by applying a bit more pressure on the head of the razor but this actually causes more problems than it remedies. Point 2: Make sure you're not applying excessive pressure to the head of the razor.

If you only shave once or twice a week, it also sounds like your beard reduction with just a WTG pass is inadequate. What I mean is after the WTG pass the stubble is still a bit long to go immediately to an against the grain pass. Were it me, I would do 3 passes on this area: WTG, XTG across the grain (like from the center line of your upper lip out towards your ears) and the third pass would be ATG. Adding the new blade and an additional pass to further reduce the length of the stubble before you go ATG should fix the problem. Point 3: Add an across the grain pass to further reduce the stubble length before going against the grain.

Hopefully these tips will help. Sorry I can't be any help on soaps as I'm not sure what is available in Canada.