That does bites Jeff. Sorry to hear about that.
I too, learned the hard way with these GFCI and their unique sensitivity. I lost game meat also one time...ONCE!
Code usually requires any convenience receptacle 6' or less from a water source to be gfci protected. Basically for bathrooms, kitchens and washing machines.
My freezers are on normal receptacles with pilot lights in case the power goes out on that line, it is easily noticeable.
About wiring from the line side...
I am pretty sure when the GFI trips you will not get power out of that device. Line or load side until you reset it. It would be of no use if it tripped and remained operational delivering power. Yes, the wires in the box will still be hot, but the slots for the device will be dead until the reset button is pushed.
Just plug in the freezer to a normal device(non GFCI protected) and you should not have any issues in the future. You can use an extension cord, just make sure it is of the proper gauge wire. Don't use any flat, lamp cord type extensions.