For those next couple of degrees, here's something you can try for no great cost.
Right now, you are getting a lot of insulation from the air around your glass sump. [Measure the difference between freezer wall temp. and the water temp.] Try stuffing paper or rags down between the freezer walls and the glass, then wetting them to get better thermal contact between the freezer and the glass. If that works, you may want to consider buying pads of open-cell foam to perform the same function, and rig a sump to keep it wet/frozen.
I was not clear on why the freezer cannot be made to hold water. Even if only up to the thermostat, water would be a lot better heat conductor than air, I suspect.
You might also see if efficiency improves by blowing some air over the warmest parts of the outside of the freezer case. Finned aluminum heat-sink material is often available at electronics surplus houses. Some fins attached to the outside of the hot case could make a big difference, if the fins are oriented so air flows up through them by convection (slots vertical).
Planning a heat-pump system is a bit like a flowing water system. You need to look for any thing that is slowing or obstructing flow, anything that is diverting energy where it isn't wanted, and take appropriate measures to fix each of them. [You guys are taking me way back to my undergraduate courses in thermodynamics and fluids.
]
Wright
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