Someone should design a mower patterned
after a cow: More than one stomach (or mulching chamber, as it were).

A decent 6.5 bhp mower like the Ariens will basically deal with anything up to
a foot high - just take a pass with the wheels set high before trying to cut it
to regular low height. If you try to grind it all in one pass, I imagine you
could choke just about anything!