Just brainstorming here:
I've always thought that the strats should become the primary targets, and the fields secondary and purely strategic targets.
Perhaps a system similar to Battlefield 2: Project Reality's "Assault and Secure" would be a good solution, which is a modified version of Battlefield's "Conquest" setup. This would help generate a battlefront while still requiring players to both attack and defend one or multiple points on the map.
For those who don't know, Battlefield 2 is a first-person shooter. To win in "Conquest," you must own enough capture points to run the opposing team's tickets to zero. The more points you own, the faster your enemy's tickets diminish. All the points in "Conquest" are open for capture at all times.
Project Reality is a mod for BF2 who's emphasis is on realism and military tactics. They modified the "Conquest" setup by making it so that you have own one or more prerequisite capture points before you can proceed to the next point. If you lose one of the prerequisite capture points to the enemy, you can not longer take the next point. You must then regain that point before you can proceed. They call this "Assault and Secure."
Thoughts?