Can the Allis pull the mower? That'd be a solution.
A bigger diameter wheel will ride over uneven terrain much better than a smaller wheel. That's particularly true of ditches, where a big wheel will bridge a ditch that a small wheel will sink into. With bumps on dry land both have to ride over it, so both will push you upwards. I expect the Allis also has deeper tires - so more sidewall flex available, and a heavier machine so it'll force more bend onto the tire rather than reacting so quickly to a bump.
According to tractor data the Allis is more than double the weight, and has 13.6-28 tires (I can't do tractor tire sizes well, but they look a lot bigger than a 2601). It's also a 40hp machine, so should run a bigger mower if you wanted.
Did you answer the question of why you have your tires filled? Is it worth emptying them and seeing if you get a difference?
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