At face value, I agree with your first comment. A bush hog is just never going to be a finish mower...
As to your hay issues, you are spot on. I love disc mowers, but they simply have to be adjusted well to accommodate each grass type. And never too low - the mower is not a plow, and simply put...it ain't worth the gain you get. But, if you like the guy you're working with, maybe he's trainable. Here's a good summary of what you are alluding to (and each year our KY extension agents try to drill this into our heads...):
GALENA, Mo. – There are many reasons to avoid cutting low when mowing hay, but money is the main one, says University of Missouri Extension agronomist Tim Schnakenberg. Schnakenberg recommends a height of 4 inches for cool-season grasses like tall fescue, bromegrass, orchardgrass and timothy and...
extension.missouri.edu