This is not correct. Typically a refrigerator will only get "so" cold because the thermostat is configured that way. Fundamentally, the only difference between a refrigerator and a freezer is where the thermostat is set. Both use a compressor to remove heat from the interior. By bypassing the...
You may need to disable the builtin thermostat on your fridge. Sounds like the fridge is cutting off the compressor at 40, instead of continuing to run the compressor whenever power is applied (by the controller).
Depending on your budget/what your buddy costs, it may be more economical just to do a point-of-use tankless water heater rather than try to plumb across who knows what. They come in a variety of capacities, and if you are having an electrician over anyway, might be cheaper to have him do...
I am not much help on the electric side of things, though I will say that an induction burner would help out if you ever needed an extra strove to cook things besides beer, say if you are hosting Thanksgiving or something. I would also definitely go 240V, regardless, just so you have capacity if...