Hmmm... I'm not a pro, hell I am barely a noob... so I was just thinking what I would do in your situation.. right or wrong..
You have FOUR boxes of bees, and its the weak hive??? Its only the end of August, should still be a fall flow coming in... fifty bucks for a new queen to build up through the fall flow, and if that's not enough, feed like the dickens through October to get them stores.
I think I would conglomerate the boxes down to whats necessary.
In Washington... probably gets colder sooner up there, so maybe feed 2/1 syrup closer to the end of September? not sure on the timing / temps. I have read that as long as its over 50 deg F you can feed syrup.
Conglomerate the frames/bees into three mediums, two deeps. Remove empty frames, put frames of brood, pollen honey into the remaining three, paying attention to the order.
FIND the queen, get rid of her. Remove ALL queen cells, and have a mated queen ready. You lose two or three days that way, instead of four weeks.
Pile the dry sugar on top the frames when you cant feed Syrup any more and hunker down...
Its 50 bucks.. I can get local queens for 20 bucks here through my association.. don't you have a local beekeeping association that will help you? If not.. as I said, its 50 bucks not much to save a hive...
In a worst case scenario, THEN combine.. but four boxes seems a lot. I have never tried to combine that many. I would think you had enough with four boxes of bees to make a go of it at this point. If you do combine, you can always get a new queen in the spring and split them to start over. So your not out of options.
As I said, I am just a noob. My area is a bit south of yours, so take both into consideration. Hopefully one of the veterans will step in and tell you if I am full of poo or not soon!!!!