>>2. send people in heavily armored rather than heavily armed. If you can make your SWAT team immune to bullets (such as by, say, encasing them in an Armoured Personnel Carrier), then they're not going to be feeling threatened and shooting anyone.

It's way easier to figure out ways to pierce armor than it is to develop it. Green-tipped ammunition is more than good enough to pierce all common and easily-worn body armor today.

Besides, if you send people in heavily armored, they are going to feel threatened by nature and will be more trigger happy.