First ya gotta start with the right ph. Usually lime tilled in takes care of that, but confirm it first, as previously recomended.
Second, what kinda hay? Grass, Alphalpha, Timothy,... They can all be simmilar in tonage, but different ph balance optimums for each. That will have an effect on tonage. Plus how long do you plan to farm it? We usually have to rotate our Alphalpha every 5-7 yrs to put the iron back in the ground. (winter wheat, or corn). I'm no farmer, I was just a cowboy, & got stuck in a tractor on occasion. (bigngreen even worked on them, but I didn't know him at that time). Anyway, like I said, I'm no farmer, but a little more info would help predict aprox. Tonage. Then take "x%" out for loss, due to rain/mold or whatever etc.
Also your posts say UPSTATE, I'm asuming New York, rainy as ill get out, but earlier, & later growing season, & harvest. I'd guess 3-4 ish cuttings per year, simmilar to western Oregon, & western Washington st. They typically have a much lower nutritional value per ton vs the east sides of those states, due to soooo much rain. Later cuttings produce the most nutritional value, but have the least tonage. You probably already knew that, or you wouldn't be as far along as you are now. Sorry, I went rambling again...