I actaully use the PE's Luftwaffe doctrine, get fallschmjagers, and then deploy behind their defenses. Once i destroy/ broken their defenses, I often follow up with PzIV support tanks with the armor and Mg upgrade, and then rapid fire my way through any infantry blobs or lone machine guns.
Don't try to arty them, they do it much better, and also, Tank destroyers is easily countered by 17 pounders or Sherman Fireflies.