A stone on a keyboard? That doesn't make much sense; in that perspective you can just throw rocks at your mouse for Cookie Clicker, or have 50 of your friends smashing the W key for you in Minecraft.
Sprinting in mid-air should just be a glitch; it doesn't sound vanilla to me. Perhaps it will be fixed in the next update?
As my time during a moderator, many mods were confused about whether or not BSM actually allowed you to sprint sideways or backwards (even the owner apparently). You cannot sprint backwards/sideways in multiplayer, it's just that simple. BSM seems to be the "fixed" version of the vanilla toggle sprint, however it does give you an advantage in PVP where the toggle is held through swinging your sword, which allows for more crits.
Honestly, BSM will never be allowed by MCSG. It's a mod/hack, which gives you an advantage over others. If BSM were to be allowed, not everyone would be able to install it as well seeing as there are numerous people on the servers who may not know how to install a mod. Optifine is optional as it depends on your GPU/CPU, but BSM would have to be required if you want to compete against other BSM users.
I've fought BSM when I was a mod, but it's clear that the MCSG administration has made up their minds. It'd be simpler to just drop the topic.
Your truly,
ShootToMaim.