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I haven't looked real close at one, but you might take a look at the lift/carry devices for electric four wheel mobility scooters. They are about the same size and weight as a Bobcat. They're the closest commercially built item I can think of to get ideas from if you are wanting a single point lift.
I beleive standard ClassIII can take 350 pound tongue weight.
If it is a 'weight distributing' Class III I beleive 500 lb. Be careful here as I recall this type of hitch works in conjunction with bars on a trailer to distribute the weigh thus increasing the Tongue Weight. The physical hitch under the vehicle would have 2 long bars that extend and mount forward of the rear axle.
Also note that Tongue Weight would be weight measured on the ball in a normal mounting configuration. Moving the weight felt on the hitch farther back may decrease the rating.
They make 'racks' that slip into a trailer hitch as you may know. I have one and rarely use it, because the ends 'droop' a bit from the weight.
The more I think about what yer doing ... the more I think a trailer would be wiser.