I can advice you that you need braces before surgery for sure. they need them so you can fix the bands to and also keep the jaws in correct position post medical procedure.
I had braces on for about 7 weeks before the operation date, and it was fine.
Now I have a splint and bands for 2 months, then they will be removed 8 weeks after the operation.
I can fully recommend Dr Hernandez Alfaro at the Instituto maxillofacial, Teknon hospital in Barcelona.
This is the guy, he can perform the best surgery in Europe for sure. maybe the best place in the world.
He also does nasal adjustment / reconstruction part of the operation, but make sure you say at consultation that your not happy with it and you want it corrected and he will do the best possible adjustments required (within reason) I think from reading many threads and posts on this forum it sounds to me that people either don't say, forget or to scared to ask or tell what they want.
in my case I had a problem breathing all my life, and he do straighten the inside and clean out any obstruction so I can now breath through both nostrils for the first time in my life.
I can only recommend from my own experience, I don't know this other guy or other doctors you list.
one thing I can say is forget the UK, they are time wasting and can't or wont do the surgery to the level of professionalism that Spain can offer. I started out in the UK they wasted over 6 months of my life. I am so so glad I went to Barcelona,
and last thing never forget about the golden rule, you usually get what you pay for. therefore a cheap option is not always the best option.
In Barcelona they basically do 2 operations in one. its not nice for the first week on liquid after but everyone has to go through the first week of recovery.
stay fit and strong, if your not already I recommend you eat / drink healthy and train in sports it will help your recovery.