Is there a way to instantly cool down Greater Powers in a place where I can't wait?
Solution 1:
LFox' 'No Racial / Standing Stone / Vampire / Werewolf Form / Nightingale Power Cooldown' set of mods should be able to allow the game to do that. (Those mods don't support the Dawnguard and Dragonborn DLC greater powers, though.)
The mod, Shouts & Powers Enhanced works with DLC greater powers, but also modifies dragon shout cooldown.
In this mod, you can shout as much as you want. There's no cooldown on any shouts, or on any powers. Before you could only use a power once a day. Not anymore! There is a 2-3 seconds cooldown on the powers and the shouts.