For those how don't know taylor vortices are formed between two cylinders normally with just in inner cylinder rotating.

I am using both CFX4 and an inhouse code to model turbulent taylor vortices and have produced almost sensible results with both k-e and Reynolds stress models.

Any suggestions of what I should try next?

Have you tried a closed or an open system with an additional axial flowrate -that means s.th. like a continuous reactor system- ? I've tried it out (self programmed code in 2D with chemical emulsion-polymerization reaction) and found interesting time dependent wave patterns, so I couldn't obtain a steady solution for the continous case. But this was all for the low Taylor-Number regime (Ta less than 100). The whole system becomes even at this laminar flow conditons very quick "chaotic" -> P. Choosat (1994): The Couette-Taylor Problem, Springer Series in Applied Mathematics Sciences