I had a lesson from a JCR student years ago, and the first thing he told me was not to worry about where my hands were because what was important was the quality of the contact. So yes, I do carry my hands wherever I need to to maintain the quality of the contact (as best I can), but in spite of what others think they're seeing, it's not because I can't keep them steadier, but because that's not the way I want to train this horse.
My idea, which seems to be working out now that he's calmed down enough for it to work out, is to allow him to find his balance without trying to stabilize his head with the reins, because I think that as he is able to sustain his balance then the position and stability of his head and neck will reflect that balance. So as he becomes balanced enough his head and neck will stabilize without me needing to hold it in place, which I'm hoping will help avoid the dreaded btv. :-)
A horse can be straight and forward and going correctly on a loose rein. Kande is right about that. That's not dressage though. The input from the rider and accuracy of riding needed for the horse to seek contact isn't there.