I did a quick search but I didn't turn much up. Is there a lawnmower that has 4 wheel drive that doesn't cost an arm and a leg? I saw the JD x700 series. Nice tractor but it's $12K. I was hoping there would be something around the $6K mark. I do like the JD X500 series but it's 2WD with the ability to lock the differential. That may be enough to meet my needs plus it's 4-wheel steer. I do not have a hilly landscape but I do mow enough ditches/driveways/culvert areas that I get stuck quite often just from being too light in the rear.
There is the Husqvarna R322T AWD. It's all wheel drive and handles steep slopes very well. It's also very nimble around object (articulating steering) and the mower is in the front. However the mower widths that are offered are a 48" side discharge and a 41 inch Combi 103 deck for either mulching or rear discharge, and it retails for about $5400.
I got two of them and like them much better than the two Wheel Horse GTs they replaced. My WH GTs did not have enough traction on some of the steep slopes I mow, but the R322T hauls my 275# butt up and down those steep slopes, forward or backward and has plenty of traction and power. It's a lot of fun to drive too.
Not sure you'd want to mow two acres with a 48" or 41" wide deck though, but I bet it would be great for your ditches/driveway/culvert areas.
I mow at least 2 acres because of the two properties I mow, but I'm retired, and having two R322Ts so my wife is often mowing too.
I tried to find a video of a Husqvarna R322T AWD mowing some steep areas but could only find this articulating AWD Jonsered, which is basically the same machine as the Husvarna R322T AWD.
It will at least give you an idea how these machines do on steep slopes. The mowing deck on the Jonsered (in the video) is the same Combi 103 mowing deck I have on my R322T machines.
Part 1
https://www.youtube.com/watch?v=vMfAAoaLur0
Part 2
https://www.youtube.com/watch?v=KZQ3cbD0rPY