For current permit requirements, I'd check the website of the US Forest Service district (or National Park) for whatever location you might consider in Washington — and even call the office to verify info on the website.
For example, here's a link to the permit requirements and procedures for the North Cascades National Park —
http://www.nps.gov/noca/planyourvisit/permits.htm
From the above page, it appears that you can't reserve a permit at that National Park in advance, and permits are issued on a first-come-first-serve basis — with limited permits available as applicants take up available campsites with their itineraries.
As for bugs in September, it's been a long time since my five or six trips into Washington backcountry (twice in the Enchantments, twice in North Cascades NP, once in Glacier Peak Wilderness area, and once near Lake Chelan), but I recall that bugs weren't a problem real early in the summer (before the snow melted a lot) or in the fall (mid to late September, long after the snow melted).
Accounting for the snow melt factor of course is a function of snow conditions for the particular year. Seems Washington this year might be having an especially early snow melt, so September may not be too buggy.
Here's a link to a trip report describing a mid-August 2007 quasi-loop trip of about 50 miles (six days) in North Cascades National Park — with the first 5 miles or so being retraced to the trailhead to conclude the trip:
http://www.summitpost.org/copper-ridge-whatcom-pass-backpacking-loop/335866
Briefly summarizing that trip: From Hannegan trailhead (which is on the west side of the National Park, about 50 miles inland from Bellingham, WA, which in turn is about 100 miles north of Seattle's SEATAC airport), go east over Hannegan Pass (about 5000 feet), northerly along Copper Ridge, down into the Chilliwack River valley, and from the Chilliwack gain altitude up Brush Creek easterly to Whatcom Pass (about 5000 feet), then start the return by going back down Brush Creek to Chilliwack River again (crossing it on a cable car this time), back up to Hannagan Pass (closing the loop) to return about five miles or so to the Hannegan trailhead.
As noted above, I believe that the Hannagan trailhead (the start point & end point for the quasi-loop) is about 150 miles or so from SEATAC airport.
My past trips in the above areas have included Hannegan Pass & Peak, the Chilliwack River valley, Whatcom Pass, as well as Little Beaver & Big Beaver valleys on the east side of Whatcom Pass, on to Ross Lake.
Another 50 mile semi-loop trip (which I've done) is to take a boat taxi up Ross Lake, get dropped off along the lake shore at the trailhead for Little Beaver Valley, hike from there to Whatcom Pass, drop down the other side of the Pass to go down Brushy Creek (halfway to the Chilliwack River valley), then backtrack over Whatcom Pass to exit via Big Beaver valley to arrive at a prearranged pickup by boat taxi at the Big Beaver trailhead along Ross Lake's shore.
I suspect the drive from SEATAC to Ross Lake would be quite a bit longer that the quasi-loop trip described in the above-linked trip report, though.
Haven't done that linked quasi-loop trip yet. But it's on my list.
Note: per the trip report linked above, bugs were terrible in mid-August 2007.
