It's been at least 2 years since I played CMBO.
The Carentan operation was one of the best times i had playing CM. Ok, first u don't fight pillboxes with armor, that's just suicidal. Kill fortifications with infantry. If I remember correctly I split up a platoon into teams and ordered them to go behind enemy lines. There they did recon, took out a few pillboxes, a halftrack or 2, and run into a company hq and killed him. Whacked some arty spotters too. And about the arty, aside from killing the spotters, all u can do is stay hidden or move from 1 place to another.
P.S.
I had more fun playing as the Germans , but that's just me I'm better at defending than attacking.