Dave, is there an existing generator compartment you're putting this into? Did it originally have a generator? Did you look at the Onan Microlite 2800? Available in either LPG or Gasoline versions. It's dimensions are well within yours: RV generator set Quiet Gasoline™ Series RV QG 2800
and it's rated amperage is around 23 amps which is more than sufficient to run your single roof A/C unit with plenty of spare power for even a microwave.
This little unit is commonly mounted on Class B conversions in some cases underneath just behind the rear axle but will do just fine in a proper generator compartment with an open bottom.