Hi Alex,
Yes that’s right, it’s much easier if you can get the finger and thumb grip, as you say they do move up about 45 degrees to allow the wrist to be free and flexible. With practice and when you get used to this grip you shouldn’t have a problem changing back to your normal grip quickly and be ready for the next shot.
Like a lot of things if you really spend time working on serves and the recovery it will improve! Let us know if you need any more advice in this area or feel free to send us in videos so we can have a look at you serving.