Westcoast Canada flight training is about to enter the dead season. Fog the whole day. Occasionally it'll clear up by noon, but then it's night time by 5pm. Theres been some airports that have been fogged in for 8 days straight. Also, I'm not too sure about accommodation for the flight schools here.
But if you're fast and you're one of those quick learners who finish their PPL in 5 weeks, or CPL in 9 weeks (from 0 hours), then you should be able to finish it before fog all the time.
Having 6 weeks is cutting it really close. I don't know about USA standards (Besides the fact that the main exam you're given questions and answers for it), I know in Canada, the only way you'll ever finish your PPL in under 6 weeks is getting extremely good weather everyday, flying 2-3 flights a day, studying constantly, and working very very hard. You won't have a life for those 6 weeks. You'll also have to find the right instructor who can handle that sort of training and will stick with you the whole way so another instructor won't waste your time trying to figure out how good you are.
However, $11k should get you pretty far if all you can do is 6 weeks of training, in Canada, for the required 45 hours, you get that for about $6k.