Approaching the problem from a slightly different position, you could pont point your student towards a Masters' thesis:
M. A. D. Robalo, 2009, Galois Theory towards Dessins d’Enfants , Master’s thesis, Instituto Superior Technico, Lisboa.
There are some more or small errors, and the aim is slightly different, so the task might then be to rewrite that (slightly too SGA1 based perhaps), to check for errors, adapting it towards the aims that you have in mind and bringing in more Riemann surface stuff.
