What you might go for is to make damage seem like it's worse than it actually is. Not sure how it'd actually play out in practice, but consider this: A player has 50 points of health, and a 25 health regenerating shield. Doesn't actually have to be a real energy shield or behave any different than normal health, it just has the mechanics of one. So if depleted, you take health damage from subsequent attacks, by avoiding damage for a time, it recharges, but the other 50 health does not regenerate. Second, when the "shield" is first depleted, the player takes heavily reduced damage for a few seconds, to actually make escaping or taking cover viable. Lastly, during this time, make the damage flash appear as though you're still taking full damage, maybe even more than you really are, to encourage running away.
You'd have to tweak the numbers, add special cases for different types of damage, and it could probably be used to the advantage of anyone who knows the system, but the general idea is that whenever someone is taking fire, it feels like they've taken a lot of damage when they get hit. Their health is low enough that remaining under fire will kill them, but it's still possible to duck in to cover. If they remain out in the open and return fire, they'll be at a disadvantage because the other player shot first, and the other player still has their "shield" and couple seconds of safety to get through.
If you want to shut down crouch jumping (more than the default increased damage), you could utilize weapons that have higher accuracy when stationary, and tune them to suffer significant penalties when airborne. This would also encourage fighting from stationary cover rather than dodging.
