Seadog, thin ringed, as in half the thickness of a subbie, and i can assure you that they were addressed as Mr, At R.N.A.S. Anthorn, HMS Nuthatch we had one and if you did not address him as Mr then you couldn`t believe the bollocking that you would get, I have recieved it.
I think you will find it was as much that they were very proud of their Branch Officer status and did want to be seen as special and apart.
I spent a year in a wardroom with an SD Lt who had been a Branch Officer and one got the impression that he felt he had lost something by becoming just like the real pigs. Certainly in my time even SD officers would make it plain they were SDs as they felt in many ways it enhanced their personal wellbeing.
HH you are correct for officers, but GIs don't wear them either now. Any way What we now call ones are old fives. The original new rig charts did include gaiters in rig 1A.
DD you are almost correct except the "Colour Warrant Officer" carries a Cutlas as does the Chief in a White Ensign Party. A Colour is carried by an officer, an Ensign by a PO. (Don't even begin to think we do things exactly the same as the Army.) In both cases the escorts are two killicks with rifles and fixed bayonets.
All this is totally off thread so to go back to the original. I have traced a relations rank progession in old Navy Lists. It went like this.
Warant Telegraphist (Mention in Dispatches, HMS NORFOLK, Bismark Action)
Any one not saluting him at any time would have been reemed a new back passage with a morse key.
If you go far enough back, Surgeons, Pussers, Chaplins, Masters and I think early engineers were all Warrants. (If you want my opinion they still should be.)