Go airborne for clusters of german armor. call in major recon plane for scouting pass, wait 4 seconds, call in airborne rocket strafing run behind it, then m8 howitzer smoke the AT guns(or smoke any AA before the planes come in), major arty call if you have the muni, charge your infantry up with MG and AT guns, airborne drop onto their AT guns for decrew and smoke concealment, plant any demo charges you see worthy, snipe with Jackson behind your infantry push, they should be pretty messed up and scattered by that point.
retreat any hurt infantry back to your major, use the sherman's jackson to hold off any counter attack if the german's think they can counter your push. If they charge you, armor piecing rounds on jacksons/AT guns, keep smoking their AT guns, if their armor is close to dead charge shermans up for the finish/spotting for jackson, pop smoke to block AT or retreat them.
There is a rather high munitions price tag on the strategy you suggested there. If I could pull that off it would be great but if I fail then I'm down a crap ton of munitions.
I think the main problem with this map is the river in the middle. Its hard for Allies to chase retreating enemy armour because they will slow down to cross the river, allowing ample time for Axis tanks to retreat to safety.
As an Allies player, I will always have that map vetoed when playing team games. Its simply too Axis favoured.