the hitch you've marked is probably a bolt on affair. they'll need to drill a few holes in the frame etc: but if that is a dwg of the exact hitch it looks like it may get bolted to the bumper. not sure if that'll work. but let me make 2 suggestions:
call uhaul one of their bigger service centers. they will install and likely wire your car for lites/brakes for the same 220 if not less.
the only down side to a hitch is the ground clearance loss. i put one on my 89 lincoln town car way back when and i used the heck out of it but it would bang the ground if i had passengers in the back seat.
next i would call general rent a car. when i've wanted to move or deliver stuff i rent a pickup from them. usually with free miles and much less per day.
good luck on the move
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