Yes I said HP but i really meant Torque, torque loss is the real issue with massive multiplication of speed.
Ultimately you were not wrong in that one cannot magically increase the entropy of the system by changing pulley (or gear) ratios. One can only convert, trading one characteristic for another. Where one characteristic goes up, another goes down. So let's look at the specifics of this case:
An engine spinning at 3600 rpm requires 23 ft-lbs of torque to make 16 HP. (Theoretically.)
A PTO spinning at 540 rpm provides 204 ft-lbs of torque to make 21 HP. (Again, in theory.)
So if we increase the speed by a factor of 6.6, we decrease the available torque by a factor of 6.6. IE 204 ft-lbs @540 becomes 30.9 ft-lbs @3600.
And 30.9 ft-lbs spinning at 3600 rpm is <insert drum roll here>: 21 HP. Entropy is preserved.
Of course, in the real world there will be lots of energy "lost" (ie: radiated as heat) due to friction of the belts on the pulleys and shafts in the bearings, etc. But there might be enough surplus to end up with the required 16hp input to the generator.
I think the bigger problem with this plan is the lack of regulation. As others noted above the genset as a unit regulates engine speed and power based on demand. With no real feedback to the tractor engine I suspect the power produced will be quite "dirty" -- voltage and frequency will fluctuate with load. Could be used in some applications, but whatever is being powered better be very tolerant or very constant.