After such a bad start, the basil situation seems to be looking rather promising.
I tossed out the crummy Mr Basil plant I bought from Loblaws.
Later, Dad and Heather bought me a plant from the garden centre. It seemed to be doing pretty well, but was limited by being in too small a pot. It just seemed to dry out far too fast.
So I bought another plant from the Byward Market and planted both in this larger pot. Aside from the soil that came with the plants, I used 100% compost.
After just one day of watering and plenty of sun, it's looking pretty good so far.