If the amps won't go low enough it means either there are other loads or else the AGMs are sulfated, or...? Would a wiring issue that increases "apparent battery R" cause that?
A compressor fridge implies an inverter. If the inverter is left on even with the fridge off, it can draw amps if any other 120v items are on. Also a small draw all by itself when on. (Not saying JimK is unaware of that)
EG, it is easy to forget the television is still on when it is "off" unless it is unplugged.
When whole house on inverter, the 120v circuits can pull amps even with nothing on. GFCI receptacles are "live" for instance.
Each rig has its own set of draws so 1 amp is meant as an example only.
The main thing is you can't really tell what is "battery only" without a battery monitor/ammeter, and use the solar controller amps display to estimate from instead.