Bike Hugger 

I’d buy a bike mower, but that bike with the single speed probably wouldn’t be ideal.  You’d probably need lower gears.

Definitely, a compact drivetrain, with a flywheel running the blades.

Wow, I totally plan on building something like this some day. I’d probably use bigger tires though to lessen the damage on the grass.

Or an aftermarket, xtracycle, add-on.

That thing has got to be hard to ride. At the Fort Collins Tour de Fat a few years ago there was a similar bi- er, trike for people to ride. Despite the immense fun derived from mowing plastic beer cups it was difficult to pedal more than twenty feet at a time before it would veer off into a crowd of spectators.
Maybe as a structure the replaces the rear wheel? Perhaps the folks at Xtracycle should make a PTO for more than blenders.