I've put 1" foam on our LG Inverter fridge too (also has rear vented compressor), but haven't had a chance to measure change in energy consumption yet (we shut off fridge at nite so foam helps keep it cool overnight).
My off grid mother in law took it one step further, physically moved compressor out of enclosure (to reduce heat transfer to cold side) and placed the fridge's condenser heat exchanger in a tall insulated chimney located out doors. That really upped the efficiency due to lower T environment outside, and thermal draft in the chimney. They had to drain and refill the refrigerant though to extend insulated lines out to the chimney heat exchanger. Sort of a "mini-split refrigerator" concept. Worked (works) well!
I'm thinking of doing sort of the opposite, bringing the outdoor air in to the fridge. Our fridge is on a corner of an outside wall. Nothing stopping me from putting in two vents through the wall and building an insulated chimney duct in the corner. The LG has two vents on the back, air intake on one side of the back, air out on the other. I could put pipe foam gaskets around the edges of each vent on the fridge, make matching ports with air in through the bottom of the wall and with air out at the base of the chimney duct which would go up and out at the top of the wall, roll fridge back in against exterior vent openings making seal with foam gaskets.
By using smooth bends and removing the crude hardboard grille on the fridge vents, plus chimney draft effect I think I could actually improve air flow and also get the benefits of cooler outside air (in Pacific North West, on a north wall so outside air always colder than inside).