My grass is rough too but I have a 15HP Stiga Park Compact HSP mulching
mower with hydrostatic transmission that copes with it well - as long
as I a) get the first cut of the season in by very soon now and b) mow
regularly.

I bought it new last year for £1700 which isn't the cheapest in
absolute terms but is cheap for a ride-on mulcher. It was a special
deal from http://www.grassland-services.com/detail.asp?prodID=255

What I like about it:

- Very powerful in its class
- Very reliable
- Big wheels, tractor treads
- Articulated body - turns on a sixpence
- No emptying!
- The mulch disappears! I never walk any into the house.
- Easier to clean tilting out-front deck

What I don't like about it:

- Too much power! Sometimes get skid marks on wet lawn
- Tubeless tyres - punctures not easy to fix
- Will dump long grass in slimey piles
- Articulated body demands respect on slopes

Overall, I would recommend this mower. Not emptying a grassbox has
transformed my life!

Stan