What if the cart provided more health (currently it provides 10 a second)? The flank classes could return to the cart during the team fights instead of to health packs and push the cart while doing so, making pushing the cart a part feasible during a fight rather than before/after, and if the cart provided noticeable health then theoretically (though theory often falls short) BLU would have a decent health advantage to offset the player advantage.
That being said, I have no idea how feasible this is for a map editor to do and this is only theorycrafting.