Does she have turners or racks to go in it yet? As far as freon and such, not sure I'd mess with getting rid of it or the compressor. Unless you decide to use the existing fan system. I would use a shelf system to isolate the heat source and fans. How many eggs are you wanting to incubate at a time? I'd be more than happy to help as I've built plenty of cabinets, but never out of a fridge. First thing I tell everybody is to decide how many eggs they want to incubate and design around the turner/racks they want to use.
I was actually thinking about this the other day but with a full size stand up freezer. What I'm kicking around is leaving all cooling system/fans intact but using the heat off the coils/compressor as the heat source instead of blowing air through the condenser. The 110v window ac/heater combos use this type of setup to heat/cool. I'm not sure it would be enough heat but I have an extra freezer to play around with.