Here's an idea which may, or may not have been thought out already.
Make the cooldown 2+ minutes and allow us to synth during matches.
Eliminate the special ammo spawns altogether.
In trials allow us to use it on match 2-4, excluding 1, or 5.
Could possibly even do this with heavy, and allow only one synth per match. Same trials rules apply.
Let's think this through and comment.
*After thinking on this for a while in the gym, I like it even more. TO THE DEVS: This gives the player control over when they receive and use special ammo. Sure it's probably at the same frequency, maybe even less. But the player chooses, not the teammates, or the game itself.