fcch - in the UK the use of two flies, a dropper and a tail fly, is quite usual though tends to be more common on the smaller rivers than the large. There are some places where you will find restrictions on hook size and weighted flies, and also on the number of points on a hook, too, but this is not particularly common and tends to be set by the owners of individual fisheries rather than by law.
It is possible to dibble with a single fly, but the effect of the water current on the tail fly (and leader below the dropper) helps to keep the dropper skimming in the surface film, particularly in rough water or with a wind. On the other hand, the dropper seems to draw the fish up and provokes splashy rises but many fish actually take the tail fly on the way down.
Would your regulations permit the use of a piece of wool, mounted either on the dropper or the tail, in place of a fly? You could more or less replicate the technique this way, although obviously some fish would take the wool, whichever position it was on.
wrke - following up on your post, which sums it up neatly, I would just add one further small point. As a left-hander, I will sometimes switch my rod to my right hand after making the cast. From the left bank, if I want to fish my fly slowly it is easier to hang it out in the river with the right hand up. In those conditions it is almost second nature for me to throw an upstream mend immediately after casting, and then pass the rod to my right hand.
By contrast, if I wanted to place a belly in the line and accellerate the fly I would have the rod in my left hand, even if I were casting right handed (still assuming I'm on the left bank).
Reverting to Anne's picture, I would certainly want the rod in my right hand to hold the line and fly out over the stong current. This would be particularly true with the dibbling technique, where you sometimes hold the rod up and out almost at arm's length to control the swing.