JD X500 with HDAP rear tires (instead of the OEM turf tires) will do exactly what you want and for a long, long, long time.

I have a 2005 GX335 with 320 hours on it. I believe that the X530 would be the closest match today. The biggest differences between mine and the X500 suggested by justalurker would be power steering and a hydraulic deck lift. I have lots of slopes up to about 25 degrees and it has handled it well all these years without any problems or issues at all. I have turf tires on it and considered changing to HDAP's but haven't done so yet. For my use, it never slips when I have the differential locked.

Sometimes a buyer can get the JD dealer to swap the turfs for HDAPs at no charge. The turfs on my X500 slip often with or without the diff-lock... the HDAPs never slip.

The best? Steiner or Ventrac. They are unsurpassed at hills. Problem is price. Used ones are a more reasonable investment. Otherwise, I think you'd be pleasantly surprised at what bar tires will do for any tractor.

i have a JD X540 w/ the HDAP tires on a 25 slope it has the locking differential... not a single problem mowing. I used the tractor w/ a 48" snowthrower to clear the driveway this winter....didn't even put the chains on the rear tires no problems. The power steering and hydraulic deck lift are some nice options, it reduces the chore factor somewhat
on a 3 1/2 hr mowing.

I have a GT225 with the tires that came on it. I regularly mow some fairly steep hills with it, and have for ten/eleven years. I have never had a problem with slipping, but I never mow when the grass is wet. I just don't do it. All I did to help was to reverse the rear tires to make the tractor a little wider.

The only other things I would do, if I thought I needed it, would be to add bar tires and wheel weights; then the biggest problem would be sliding off the seat.