Here's a summary of what's been established to my 'critical thinking' satisfaction on this topic. The ideas above are really super!
1. Consumer Report-types have weighed in that Top Door Chest Freezers are more efficient/use less energy than Front Door types. If one had a 'Thermograph'-type Heat Viewer, one would see the cold air pour out when the Front Door type is opened.
The Chest arrangement of Food inside may be less convenient, but that's an entirely different issue from Physics 101 that cold air sinks and stays there [in the Chest type].
2. The issue of diminishing return on Insulation value is up for Barroom discussion.
Off Grid and Solar Home Geeks have created some thick wall Fridges and Freezers with Walls well beyond 2". Whether that's the best use in a TD is another Barroom discussion, but folks will argue this point pro & con.
3. The 'darling' of Insulation is Thermax. For years, it's been rated at R-8/inch. Easy to cut and work with, and easy to tape edges of to form a Box. Metal Duct Tape is good for this. Perhaps lining such a box with caulked, thin wall PVC Sheets from a Big Box Store would be one way to create a solid enclosure. The 1" version sold at Home Depot is rated at 7.2 R/inch, but folks round up and down for easy mental calcuation of total R. When you're trying to keep Food in the mid or high 30's and it's 110 outside [sealed, in the Sun], R-24 or R-32 is not crazy.
Taping Thermax around a commercial Cooler is one easy way to go; especially an old one gotten on the cheap...
4. Some water is usually encouraged, since it keeps Food colder than cold air. Nope, it's not 'all the same', despite what a Thermometer might say. Case in point: water cooled Engines were/are much better at cooling than good ole air-cooled VW Bug Engines. Water has 'more' heat-carrying capacity.
5. Hard plastic, square containers are a great way to pre-freeze Ice and lift out; especially if they have handles. No space is wasted. Leave them ~3/4 full and then freeze them. Put a tiny pinhole in the cap to allow air to escape as the freezing water expands.
Much of this has been worked out prior by Off Grid Geeks. Surf those sites for ideas to not recreate the Wheel.
Energy never lost never has to be replaced, by any means. Solar Electric Energy is mighty expensive/Watt. Super Insulation means 'excess' doesn't have to be generated by Rooftop Panels [or Propane, etc.]. Everything from Bricks to a few Cases of Beer is used by Off Grid Geeks as a chilling 'Thermal Flywheel' to keep a Fridge cold. The 'right' size of flat, square water/ice container in the bottom of a homemade Cooler could serve the same purpose.
Thermax Rigid Insulation
Sunfrost Refrigerators