That's the problem with having it go across the board. It only works for control because control easily translates from thaum to evocation - they both use discipline.
Power/complexity uses Conviction/Lore.
So, if you're going to go the model that sanctaphrax suggested, then you'd use the speed of evocation and the method of thaumaturgy - Discipline and Lore because that's what your foci are based on.
If you're going with the model that Tedronai suggested, which is both speed and method of Evocation you'd use conviction and discipline.
Lastly, you could have your foci cross over (lore for thaum - conviction for evo) but you specifically have to lock in your foci that I don't think it should work that way.
It's one of the major issues I have with it going both ways. I think it's easiest to decide if your foci affect evocation or if they affect thaumaturgy. That way way you use evocation methods you use your evo foci and when you use your thaum methods you use your thaum foci.
Yea thats why I'm saying that. I guess I can see what you are saying though and that makes sense. However that goes back to a previous thread I saw about specialization. If I have to take a focus item that is evocation element then I should be able to take a specialization in that particular "element"
Well in your specific case you have sponsored magic AND evocation - which allows a specialty. I think, since you have a new "element" open to you, you could take that as a specialty...although, I'm not sure how this affects refinement. At the very least your specialties would only be applicable for evocation since sponsored magic doesn't specifically allow specializations