I wasn't even referring to the walking speed, but rather how it works. The player can't walk diagonally; when changing direction, the character first turns and only then starts walking.
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Or you can allow the player to perform client-side actions immediately upon receiving a command from the user, simultaneously sending data to the server for verification. If, for example, the player's position is suspect, you send the client a teleportation command to the location the server deems correct. All interaction checks also go through the server.
This won't fix the problem completely, but at least some actions may be more responsive even with high ping.