David, my suggestion on the sun is that you stick with what you are doing and if you don't get fast enough growth to bloom your plants by fall, you need to increase sun, fertilizer, and/or water to speed things up. If you are getting bloom by August/September, you're doing great. I don't repot until I HAVE to because I have so many. I use cheap black nursery pots (3 and 5 gallon) and most of the time the gingers will hit the side of the pot and then split it out or climb over the top. Sometimes I have to cut the pot off to repot them. I usually repot in the spring as they are going out, so that I do my root disturbance and sunburning at the same time. That way, I can place them and leave them until fall. If they don't look too crowded in the pot in the spring, I may top them off, but I don't repot. Once you get a clump going in your pots, you will have rhizomes out the wazoo and you just can't keep them all. Once the rhizomes start 'running', they keep going in the same direction, so they often leave a trail of dormant, older ones behind, with no shoots on them, with all the new growth on one side of the pot.
I have never tried grocery store ginger. I just recently got zingiber zerumbet 'Darceyi' and it has bloomed for me this fall and I really like that one. It's my first shampoo ginger. I'll see if i can find a picture of it.