I bought a Fiskars "Momentum" reel mower today and I heartily endorse it. You have to use this mower to understand and appreciate it's seemingly bass-ackwards design. The drive wheels being in the rear means they can't be lifted off the ground, and the frictionless reel doesn't touch the shear bar (though the grass does) and so the reel spins for a long time, and it is *very* quiet and very smooth.
I will try it on the really thick grass, but I'm guessing it will do fine. The reel is heavy and has a lot of momentum (hence the name). The handle is also very sturdy. The four wheels on the base move along the ground in a way that is quite different than other mowers.
It is quite different, but there is a reason; and the results speak for themselves.
http://www2.fiskars.com/Products/Ya...#8203;l-Mowers
(click on image for link)