While I have no experience with a ZT, I do experience some traction issues with my garden tractors. I have found the tire tread will have an effect on sliding sideways when mowing across the slope. Suggest comparing tire size, tread width and tread aggressiveness. I run wheel weights for mowing and snow removal.
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1863, 1864, 48" and 54" mower decks, 54" snow plow, 451 snow blower, TracVac 580
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