Are there relevant rules and etiquette beyond §E6.2.2? ("A player must be allowed to stop his clock after making his move, even after the opponent has made his next move.")
Yes, there is at least one rule in the FIDE Laws of Chess, which is related to 6.2.2 and is key:
1.2 The player with the light-coloured pieces (White) makes the first move, then the players move alternately, with the player with the dark-coloured pieces (Black) making the next move.
1.3 A player is said to ‘have the move’ when his opponent’s move has been ‘made’.
Another way of saying this is that every time you move your opponent also gets to move. From that derives another very important principle, particularly in blitz, which you should already be familiar with as a master level player. It is the principle of prophylaxis.
Far more important than clock handling is to always be aware of your opponent's ideas and how you can thwart their plans. This is important for two reasons:
- There is no point in successfully planning a mate in 2 if you allow your opponent's mate in 1. The position on the board overrides the clock until one of the flags falls.
- If you make no effort to stop your opponent's plans then they will be able to move quickly (pre-move, even if playing online). If you stop their plans then they have to stop and start thinking what to do next. This can make a big difference at standard time controls but is often a real killer at shorter time controls.
There are other general principles which are less important but also worth paying attention to.
- Other things being not too unequal try and play on the same side of the board as the clock.
- When very short of time try and make short moves close to the clock.
- Practice so that you are ambidextrous with moving so that you are comfortable with the clock on either side. Perhaps have blitz sessions where the clock is always on your weak side so that you can practice with your weaker hand.
As regards when one player is allowed to move the rules are clear. Once the opponent's move has been "made" (1.3 above), which is before the move has been "completed" (clock pressed).
4.7 When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made in the case of:
4.7.1 a capture, when the captured piece has been removed from the chessboard and the player, having placed his own piece on its new square, has released this capturing piece from his hand,
4.7.2 castling, when the player's hand has released the rook on the square previously crossed by the king. When the player has released the king from his hand, the move is not yet made, but the player no longer has the right to make any move other than castling on that side, if this is legal. If castling on this side is illegal, the player must make another legal move with his king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move.
4.7.3 promotion, when the player's hand has released the new piece on the square of promotion and the pawn has been removed from the board.
Once your move has been made (your hand has left the piece in the case of moves other than castling, captures and promotions) then your opponent is free to make their move. They do not have to wait for you to press the clock.