Some years back you could mail (USPS) food boxes to some of the ranger stations near the trail. I recall we mailed large boxes (there were five of us) to Mowich and Longmire (we started at White River. I imagine you still can. I don't think the rangers will carry food to a backcountry campsite, though.
We took 13 nights to do the trail and enjoyed every last minute, so far it has been the highlight of our backpacking life.
So what that we had a five mile day once and rarely hiked more than 8 or 9 miles (lots of elevation gain/loss, so that's harder than you might think). This gave us lots of time to enjoy the spectacular scenery, lounge at our campsites, write in journals, go birdwatching, take over 1000 photographs, cook fancier meals, eat leisurely, contemplate our navels, whatever.