I have spent some time pondering a solution to this as well. It feels very bad to be waiting to have your RPG ammo resupplied, only for the Support player to move his ammo box just before you replenish a rocket and have all of that waiting for nothing.
The idea I was pondering was having the cooldown progress bar start filling up, even when you are not standing on a supply crate. When the cooldown progress bar fills up completely, it will stay full but it will not replenish the gadget until the player runs within range of a supply crate. As soon as the player enters the range of a supply crate while the cooldown progress bar is full, the gadget on cooldown will be replenished. I will refer to this as the passive replenish speed.
To better reward players that spend time waiting within range of the supply crate, the cooldown progress speed could be doubled while within its range. I will refer to this as the active replenish speed.
I figure the active replenish speed could mirror that of what we had in the beta, and the passive replenish speed would take twice as long.