If you are intending to *keep* it lush turf, you may not be able to keep as many in there as you are hoping. And it will still leave a conspicuous set of 'footprints' across the lawn behind the tractor, a couple weeks' worth til the grass regrows.
I have a 4x7 tractor (with additional 2.5x4' 'upstairs'). With just 2-3 sexlink hens in it, I still had to move it every single day to keep the effect on the grass to a manageable level. Even in just one day, it'd get eaten down pretty good, and if it was left there for 2 days there would be not much grass left and a whole lot of dirt. Even moved daily, they made bare dusting-holes here and there in the lawn, rather to the annoyance of my lawnmower-wielding husband. This is a pretty healthy and good-growing lawn, though it is not a golf-course-like monoculture.
I would suggest trying to put the *happiest* in the *most convenient* amount of space, rather than the most in the least, and not getting too ambitious.
And think about what you'll do come wintertime.
Good luck, have fun,
Pat