Here's what I did without altering the fridge.
Find the thermostat / temperature probe inside the fridge. Mine was behind the back wall. It took 3 or 5 screws to undo, and it was obvious that it was the thermostat probe on a long wire. I think it might have been near the fan on the inside back wall. Sounds like you found two? Which is interesting. If your fridge has a temperature readout, you can try holding it in your hand for a minute and watching if the temperature rises on the display. If it does, then you should have the right one. If you're just going by the circuit diagram and noticing two sensors, then try finding the one inside the fridge. With any luck, it will be in the same spot - I think my beverage center is the same one, from the look of the front of it. You should find it behind the back wall, towards the bottom, in the center (left-to-right) near a screw. Don't bother opening up the whole display and control panel on the top inside - it's a pain to get back in and if I'm right then the sensor you need isn't there.
Now that you have the temperature probe, go to ebay and get something like this:
https://www.ebay.com/itm/5v-portabl...pad-carbon-fiber-heating-pad-Pip/173238963552
In case the link doesn't work in the future, it's a $0.99 5 volt (usb plug) carbon fiber hand warmer pad. Actually, the one I got a couple of years ago came as a two-pack, and the pad was smaller, I think. So I've got a backup in case something happens.
Put the hand warmer and temperature probe in a little box (battery box, film canister, etc. - whatever will fit them).
Find an old, low-power USB charger. The ones for the new devices can let a device draw 2 or 3 amps. I think the old one I found was rated for 500 mA. Not useful for modern phones, but perfect for this application.
Plug in the hand warmer on its own plug, and plug in the fridge to your inkbird. The warmer will fool the fridge into thinking it's very warm (100+ F), rendering its internal thermostat useless - it will be in "always on" mode trying to get colder but never getting there.
That's the solution I came up with for my beverage center, because whenever the inkbird would cut power it would reset itself to a setpoint of 50F or something like that. Again, it looks like you have the same model. Now it will get as cold as the inkbird will tell it to. The thermostat on the beverage center would only allow a setpoint of 40F at the coldest, but with this setup I got it down to freezing (accidentally) one time.