I am a former resident of New York(Rochester) and even before I got into the RV life, I avoided the thruway like it was a Plague infected lady of the night. To the original poster, if you had consulted a map you would have seen that St rt 20 would have been a much better alternative. All toll roads charge by the number of wheels on the ground, not the height.
I did make a concious decision 2 years ago to drive the thruway. We were headed to Rochester from Buffalo. The only alternate was the southern tier highway, which was at least 50 miles further. At close to $4 a gallon for diesel fuel, the toll was cheaper. I had to promise my wife that I would blast the toll taker with a rant since it was my decision. I must admit my mouth was bloody raw from biting so hard to keep from telling the man what a lousy road it was. Coming from the south I avoid all toll roads that I can. I have a list of the bridges in Chicago, Maryland, and New York that I own from tolls that I paid. I keep sending the resident authorities bills for my money but they keep ignoring me. Pre-plan your trip next time.