Guys, I've got it.
You want spy mode to be about stealth? You want it to be about small battles in the background and espionage? Well here's how you do it.
1) Spy leaders only get 3-4 implants, they have a small team, this way they don't go around implanting everyone
2) Heads of staff are pre-implanted with CentComm implants and are immune to spy implants, this goes for sec too.
3) The crew is encouraged to detain spies, not kill them, and alert sec when they get them. Taking a spy in for questioning rather than killing them there can be useful, especially if they get their implant removed at robotics. This could lead to some fun rescue missions.
4) and possible the most important change to make it about stealth. Spies are NOT allowed to kill civilians. They would be one of the only antags who aren't given a free pass to a murder spree. I'm not sure how to do this exactly, perhaps a score system or maybe a strike system where after X number of murders they're spy implant kills them. By doing this the spies would have to avoid getting caught because the crew can attack them but they can't attack back, at least not to kill them.
If you do this then the spy items can be stealth items, like smoke bombs or sleepy pens. Maybe a type of flash grenade that makes all in range temporarily blind, even with sunglasses. With these changes, mainly #4, Spy would become the stealth game mode it needs to be rather than a free for all brawl.
Not all Antags need to be killers.