Why would you have to use the mini fridge? There are otehr ways to do it...
I also have a minifridge which had a 28w TEC. If you were to do this I think using more than one TEC would be best, 4 or 5x80w TECs would be much easyer to cool than one large 300w TEC. Remember you have to cool the hot side too, how would you do that?
For the heat exchanger haveing an ice block as said above might be a good idea, but with one change to make it better - get some 1/2" copper pipe, and loads of T connectors. Then cut the pipe and have 10 1/2 pipes running in parrelell - This would give you a nice large surface area. Using small lenghs would probably fit in your minifridge. you oculd use 2 or 3 of these in parrelell aswell if you have space in there! Using it in parrellell wil give you less flow restriction. A pipe used as a heat exchanger between your loop and the ice would seperate the chiller from the main loop, giving you no corrosion if the rest of your system is only copper/plastic.
I aviod aluminim compleatly, although I am using some silver, and also some solder (tin + lead) I dont get any niticable corrosion. I use pure de-ionised water. Im not and have never made a chiller. I might soon, after Ive tryed my heatercore outside in the cold
