Like the KAK pistol buffer tube this one also started to rotate when tightening the castle nut.

Unfortunately you cannot remove the brace from the buffer tube without disassembling the spring-loaded button (not going there). The use of a strap wrench also isn't happening for the same reason. There is not enough exposed rounded surface on the buffer tube for the wrench strap to gain any purchase.

Fortunately I found a solution in my dad's old Black & Decker workmate portable workbench (I have neither a workbench nor a bench vise)

Using the bench's adjustable "vise top" I held the lower in place with a BEV block and also placed the back end of the brace firmly but gently into the vise top as well (used a rag to protect the finish. I was then able to tighten the castle nut without having the buffer tube turn.

(end plate  used was a Damage Industries steel QD plate)

I usually end up turning the buffer tube slightly off center so the final tightening of the castle nut spins the tube centered. It takes a few tries to get it perfect sometimes.

I take it you are using an end plate that has no 'indexing pin' on the inside (the part that fits into the groove in the botton of the buffer tube's threads).

No, even the end plates with an indexing tooth can end up cockeyed. Sometimes you can get lucky and the tube ends up aligned vertically, but not usually. There is usually some play between the tooth and groove that allows the buffer tube to twist a bit when the castle nut is cranked down.
I tighten the castle nut down and check alignment. If the tube has turned past vertical I loosen the nut slightly and spin the tube as far in the opposite direction as I can so it spins into the correct position with the final turn of the castle nut. It can take several tries to get the tube in the perfect position so it will spin vertical when the nut is fully tightened.
A shoulder stock being a couple degrees of center won't hurt anything and it may actually be a better fit against the shoulder in some cases. I bet if 100 AR's were checked, half of them will have the stock off center a degree or two.