How can I speed up the cooldown for the helicopter homie?

There is a cooldown period after each call to a particular homie. It seems to me it is roughly the same period that your pay timer is on, though not synced.

I've finished the game (excluding paid DLC) and did not see any upgrade that offers a homie cooldown bonus.

Loading a save also loads the state of your phone homies. As well, if you're playing in someone else's game, loading a save refreshes your character instead of loading a new game, so you can recharge homies nigh-instantly.

I'm level 50 on Saints Row and still there are no upgrades to decrease the waiting time. Level 50 is the highest respect level you can get.