I think I managed to unscramble it.
I have just realised that there is one thing that I should also have mentioned. If you use a simple stack, you should probably do a false shuffle or switch the deck. I usually false shuffle. Don't make a big deal out of it. Do it casually, then into the trick.
"Proper" memorised stacks seem to have two advantages. The first is that the cards seem to be in a truly random order. As I said before, this is not necessarily an issue in practice. Also, there are some cyclical stacks that use formulae or rules to disguise the stack; they are not all obvious, even if someone does inspect the deck.
The second is that there may be tricks built into the memorised stack, such as Poker deals or spelling tricks. These may be harder to fit into a cyclical stack, but there are definitely tricks that use the cycle as part of the method, which couldn't be done with a non-cyclical stack. One of my favourites uses this principle, in fact!
There may be other pros and cons, such as the ability to get into the stack quickly from new deck order (as Mr Grue rightly remarks). I prefer Eight Kings or the Osterlind BCS, but I can see a place for the Gauci stack in my repertoire.