You say you would like to do 13 acres. That is way beyond what is possible with a ride-on mower, even a 48 inch cut.
Looks like a second hand agricultural mower is required, with at least 7ft cut. These are nearly always equipped with multiple rotating drums, with swing-tips. You can buy the tips by the dozen quite reasonably ( £1 each.)... They do a good job of levelling small bumps and mole-hills.
These mowers mount on the 3 point linkage, and are swung out to the right for cutting, but swung back and trailed for transport. Their cutting angle is adjustable, from 3inch high, right down to the white roots.
I think you need to build up your grounds-keeping equipment. If you have a 60hp tractor, that means you can tow heavy rollers and Verti-Corers if you are keen.
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Last edited by scifi; 1st Jun 2017 at 12:03.