"Only packing dry food and hoping to hike around 27 miles a day."
Good luck with your effort, and make sure to take good care of your feet and body in general. A couple years ago, a friend of mine and I did 27 mile days for 14 days, and bailed after that, with a variety of nagging aches and pains. Those long miles day definitely added up for me, with no zeros or near-o's or partial days into town to let the body recover.
There are a lot of semi pointless ups and downs on the CT, hopping the toes of descending ridges, and many more ups and downs in general. Lots of up 3,000 feet to get above timberline, only to immediately go down 3,000 feet. Not ideal.
Not to put a damper on it, but I was pretty disappointed by the CT (maybe the PCT and lots of hiking above timberline in the Sierra has spoiled me?). Lots of dirt road and old logging road walking, sometimes limited views (due to following roads in the forest), and for a number other reasons. I wish it had been a purpose built trail, instead of feeling like what it is, a cobbled together assemblage of existing trail, open roads, old closed roads, and whatnot. However, we did bail before the best part - the San Juans!