I thought that you have this mostly worked out: Bevel gear dynamic simulation
Dynamic is a good idea but it really depends on the case. Implicit should be faster but prone to convergence issues. You don’t have to worry about convergence with explicit but it’s terribly slow for large models (especially in CalculiX).
Constant speed can be simulated as a boundary condition on the reference point. Contact can have default settings for now (unless the stiffness needs to be varied, especially in explicit). Just make sure that all the surfaces that may come into contact are selected for contact pair(s).