Weakly weekly isn't going to cut it for a ginger, except maybe if you're overwintering it in the house. That's good for foliar feeding orchids and epiphytes, but not for big leafy plants that make big rhizomes.
Outside in warm weather, a pelleted time-release fertilizer is the way to go, and mine get a double dose to what the label says. Because you're also watering heavily in warm weather, the fert gets used up faster. I've never yet had any sort of fertilizer burn on any gingers. They just make more leaves.
Definitely they could take more sun, although preferably morning sun and maybe late afternoon sun. They do love the heat, and lots of humidity too. I'm originally from Vancouver, BC just north of you there, so I remember the long, warm summer days and nice cool nights. Give your gingers as much heat as you can find for them without burning the leaves.
