Here's
the modified cart in the down position, with the handle folded onto the
cart. The two pins on the table are the locking pins.
Here's
the table in the up position. Note that the release cable has been
rerouted out of the guide ring. The new handle is a bit taller, and this
change takes care of the extra cable length needed. You can see the pins
locking the handle.
To re-route the cable, you must first remove the locknut from the other side of the guide/adjuster. Screw the adjuster in a few turns clockwise to make this easier. Once this is done, screw the adjuster all the way down. This will give you enough slack to get the end of the cable out from the release lever. Then, unscrew the adjuster and release the cable. Reassemble.
Here's
the handle in the out position. The table will go under the rear part of
the machine, and let you pull the machine around. 
Finally,
the crude fix. I used four 5" 14GA angle brackets, and four M8 x30mm
screws and nuts. You could use imperial screws instead, take the M8 to
the store with you and use it to select your brackets and screws. My
next trip, I will be adding lockwashers.
I would also like to eliminate those sharp bracket edges, but that is also for later. This would be nicer with U-shaped pieces, but I wanted a solution that you could find in the hardware store.