Well, the cart would require that the character wheel the whole thing around like a wheelbarrow, with the one back leg possibly being stood upon when firing.
If you look at the historical weapon, it had a hook and two pins on the barrel. The pins were for bracket mouting on a device such as the one described, whereas the hook was to brace on the crenelations of a battlement.
All that said, 2d12, even multiplied by 4 for a full attack (8d12) doesn't even keep pace with many wizard spells that can easily pull out 25-40 d6, many of which go against touch AC or saves (also generally lower than AC, but often still dealing dmg on a successful save).
Granted, weapon special abilities can tip this scale, but it's still not quite OP IMHO, especially when you consider the investment involved. & if you don't like the cart you could always makethem vventure through passageways too narrow for it (but don't be surprised when they pick up an immovable rod as Froze_man suggested, above).