I had a chuckle reading about the concerns about size, weight, wheel base and ride quality while haying. For several years, while growing up on a small dairy farm (milked 50 head), one of my jobs was to rake hay with my grandfather's Farmall A. That thing was a whole lot lighter and smaller than the John Deere 4600 I have now. I did get tossed around a bit on it. It was still one of my favorite tractor jobs, though.
We had a couple of larger tractors than the A - a Farmall H and a W-6. I ran the hay conditioner (crimper) with the W-6. Dad usually used that tractor for the baler as well. We mowed with the H primarily, but sometimes with the A.
I don't do any haying now. I've half-thought about volunteering to help one of the local farmers, using my tractor. I'm 64 and retired from a "career" job, but back to working nearly full time in construction engineering. While I'm doing that, I think I'll hold off on the "volunteer" haying. Maybe someday.