I just finished this fight without too much trouble.
I found the "thin trees" on the east ridge to be pretty good cover, actually. If you advance through the center of the tree line, though, your troops will be under the canopy and will be visible to all. If you advance to the east of the tree line, halfway up the slope, the canopy will block LOS from the rest of the map. Mostly.
You can walk at least two-thirds of the way to the town this way and receive only spotty fire. More importantly, you can find numerous positions on the hillside where you can fire through the canopy down onto the church and to the line of foxholes that lies between the town and church. The return fire was not at all lethal.
The key for me, though, was planting a Stuart in the sweet spot mentioned above at the northern end of the tree line. From there the tank was able to drive all opposition from the church and foxholes. That then allowed me to mount an advance from the walled grove through a dead zone on the "cross valley road" and then straight up the slope to Building 14. You may also be able to get an AFV around the back side of the NW stand of trees and then pummel the town from a position north of the walled grove without getting hit by an ATG.