Hi Duncan et al.
"would not approve" referred to the choice of processor, I thought you were a died in the wool Atmel user!
I have never used a PICAXE, but assuming there are no serious overheads which prevent the full use of all the resources of the base chip, I cannot see why they should not solve mazes. I agree with the comment about all mice tending to become the same and accept that with minimal mice this process could be more rapid.
The dynamics and chassis design will give scope for originality since the requirements are not the same as a conventional mouse and there is not much processor power available to overcome shortcomings in this area. Also a small processor does not have space to optimise the route using conventional flooding, this leaves space for new maze solving ideas.
For adults and older students, a "one make series" should select a target device which is too small to succeed with a conventional approach. Otherwise you are back to the problems of handicaps.