TDI teach centre first, then right then left. My instructor for ANDP asked which way I would do it and was happy with the GUE way if that's the way I was taught.
My TDI instructors, both for trimix and for becoming a tech instructor, did not care how it was done as long as it was done
fast. My UTD instructor did not care how fast it was as long as every stop was done beautifully and in the proper sequence. When I crossed over to TDI for trimix after being with UTD, I did the most beautiful shutdown UTD-style drill I had ever done, and the instructor said it was terrible because it took so long.
In order to meet the TDI speed requirements, especially for instructor, my TDI instructor trainers (I had 2) suggested I use both hands at once, using the left hand to close the isolator while doing the right valve with the right hand and then using the right hand to close the isolator while working the left valve with the left hand.
To me, all of this is farcical because you will never do the valve shutdown drill in its entirety in a real-life situation. It is an exercise that combines all the skills you might need in different emergencies into one package. What truly matters is your ability to reach and manipulate each of those valves in the event of an emergency.
For those agencies that require the drill be done within a certain time limit--as PADI does, for example, here is a thought. PADI requires that students in sidemount be able to do the drill in 30 seconds. With my old sidemount tanks, I could not do it in 30 seconds if the tanks were on shore, standing on a platform in front of me--it took longer than 30 seconds to turn the valves all the way on and all the way off. WIth a different brand of valves, it would be done easily, so skill was not a factor.