Hey Oldboy. I haven't heard of Dr. Connely's diet, but I did go on a Psoriasis diet - whole grains, no red meat, no nightshades, no dairy, more fruits and veggies. My Psoriasis is almost gone, and I had a bad case. I'm sure its a similar read. Don't expect anything other than slow and steady, but you are actually getting to the root of the problem, and not the symptoms.
I would also recommend anything to help your liver. I had good success with the liver flush. You may want to try these after acclimating to the new diet. Also, any type of Colon Cleanse like Dr. Natura.
The diet seems restrictive and tough, and takes some discipline at first, but now I am loving it. I actually feel lucky that the Psoriasis forced me to start eating better. You discover new foods like hummus, fruits and veggies. I was a meat and potatoes before.