ScubaSeth and I played this scenario again last weekend, on Vassal. Again, he was Germany and I was USA. I won again, applying the same basic strategy Alessandro recommended; ScubaSeth acquiesced on round 5.
This time around, I was able to suppress-and-rout the two German MG squads on round 3 and 4, respectively. This really opened-up the battlefield so when I rushed my squads across the bridge and through the woods they took far fewer casualties. Then I came around the west flank with officer squads and by round 4 had the German double mortar squad in my sites. Because they were double mortar and had no expendable regular infantry to take as fodder I cleaned that up pretty quick.
Facing such resounding successes as the Americans, I'm now curious how the Germans could effectively counter the strategy I applied. ScubaSeth concentrated his units on and adjacent to the victory objective hill hex; shortcomings of this approach are that they're more vulnerable to mortar fire and less capable of enabling side- or rear-flanking attacks such as would be enabled if a German MG was placed in one of the buildings to the far NW of the map.
Another thing I liked about this set of play-throughs was how integral strategy cards are. Critical Objective was essential in getting the Americans to the objective hex faster, and I used Surprise Assault one time at the beginning of round 3 to erase the German double mortar squad before it could attack. From the German's perspective, Take Cover and Go to Ground both helped squads survive longer, while Rally Cry and All or Nothing gave squads additional actions.
My potential German play-throughs will have to wait for another time, however, because we decided next we're going to play a scenario with vehicles.