Depending on how much room you have in the surrounding cupboard, I would sugest ripping out all the old attempt and starting again with polystyrene foam as your insulator, and then for the visable inside of the box you might consider using plywood with a formica lamenated to it, the corners could then be sealed with a silicone sealer and you could fit a new drain in at the same time. You could also utilise your existing cold plate and compressor. This would give you an easy clean, profesional looking fridge and probably work out cheaper than having a stainless steel liner made up. Depending on the average temp's in the area you are, I would sugest at least 3 inches of polystyrene as this would give you a good insulation which would mean the fridge unit would have to work less there fore putting less of a strain on your battery's.
Hope this helps