If you are traveling light and willing to put in some longish days, you should have no trouble doing the loop in 4 days, especially if you are beginning and ending the ride in Saratoga Springs without the tag end leading to/from Niskayuna.
[Spoiler Alert] I did the ride with two small rear panniers and a handlebar bag, which I would call modestly loaded. My shortest gear was 34x27, pushing a 700x32 tire, which works out to something like 35ish gear inches. I would consider myself an average-strength rider, and although I wouldn't have minded having a bit lower gearing, I was OK, with one exception: a short hill somewhere past Lake Luzerne (I think) which for about 100 meters nearly had me off the bike, pushing. Even standing up, I just couldn't make it go
. The three big climbs- Graphite Mountain Road into Hague, Keene Valley to Lake Placid, and Whiteface mountain- from Wilmington to the crest- were no problem. Long and challenging, but never so steep that I ever felt that I would have to abandon the saddle.
You should check to make sure of this, but if I am not mistaken, the Whiteface Mountain alternate avoids
the climb up Whiteface mountain, which you most definitely want to do!
If it helps to break the ride into more manageable portions, there is a place called the Nick Stoner Inn near Caroga Lake. My guess is that you will have the park and your hotels/inns to yourself, and I think that the time of the year which you have chosen is perfect.
You're going to have a great time!