CuttingChris,
If the problem is spinning I'd make sure the dampeners are in good working order, check the tire pressure and slow down a little. Tire pressure can be adjusted between 13 and 18 psi in most cases to improve traction.
Often when the lawn is stressed it can easily be damaged and slowing down is required. Once the lawn is in a little better shape you can then increase your speed again. If I recall you guys have been pretty dry and abnormally cool this spring and cool now again. This can cause the grass to be a little weaker and more likely to tear loose from the roots.
The ATV or bar type tires will probably cause more turf damage that the stock tires. The big concern when putting an ATV or bar tire on a mid-mount Z is that they actually make operation a little scarier. By adding this type of tire you can (but not always) increase the units ability to hold steep hills. Hills far beyond what the mower was intended for. The real is that these types of tires may allow you climb steeper hills which would allow you to put yourself into an even more dangerous position when the tires finally loose traction.
Look at it like a sports car. The sports car will do its job on stock tires and will give a little warning before the tires let loose. Now if you take that same sports car and put a set of racing tires on it you can go much faster, where the speeds are much less manageable if something goes wrong. The racing tires will also let loose much much more abruptly with much less warning. Now youre going faster, you had less warning and youre in trouble. Which one gives you a greater chance of getting home that day?
The mower is no different. If you add this type of tire to hold you on steeper hills your taking a much greater risk and it's not worth it. If the hill is that steep then it's probably a good place for a walk behind, a push mower or a weed whip.
Thanks
Terry