Your tires are too wide for your application. When you twist one on grass, sand or the driveway, you will see the torquing effect. Look for a narrower tire or even try a very HIGHER pressure which will push out the center of the tire and increase the peak contact patch force. This will reduce the lawn tearup while turning because the contact patch width is smaller.
A great experiment would be to try to swap your neighbor's tires and wheels on your machine and see if the improvement is tires or weight distribution. My JD has a traction assist involving the deck lift to put almost all the weight on the drive wheels. This works very well. It also has an electric pedal operated diff lock that I use all the time on my hills.
Ultimately its a tire size and tread pattern problem if the weight distribution is favorable. Try moving the seat all the way back onto the drive wheels, too. I bought a set of killer snow type tires for mine that I thought would help me with hill climbing but they were actually worse. Now I run a set of used turf treads that I got from a dealer's take-off supply. Lots of tiny little 'z' knobs closely spaced. No more problems, except that the high pressure makes the ride pretty lousy.
A great experiment would be to try to swap your neighbor's tires and wheels on your machine and see if the improvement is tires or weight distribution. My JD has a traction assist involving the deck lift to put almost all the weight on the drive wheels. This works very well. It also has an electric pedal operated diff lock that I use all the time on my hills.
Ultimately its a tire size and tread pattern problem if the weight distribution is favorable. Try moving the seat all the way back onto the drive wheels, too. I bought a set of killer snow type tires for mine that I thought would help me with hill climbing but they were actually worse. Now I run a set of used turf treads that I got from a dealer's take-off supply. Lots of tiny little 'z' knobs closely spaced. No more problems, except that the high pressure makes the ride pretty lousy.