Mark, before you go nuts with a 'Stanley knife' cutting an internal lid as such.
Tonight, after dark, put a torch in the freezer.
Close the lid of the fridge, and check to see if there are any gaps letting light out around the lid edge.
If there are gaps then that's why your freezer is icing up.
I know your fridge is not an Engel, but I took mine back because of just this problem.
It's the same as leaving the fridge door at home open a crack.
Yes the lid for the freezer is a good idea, but if the major lid doesn't seal correctly, it'll continue icing up.
Good luck with it.