just curious - are you running recommended tire PSI's ? Higher pressures could contribute to the problems you noted...and mfgrs often overinflate new machines for shipping purposes.
I ran a 2560 ztr for several yrs cutting around 6 acres - had turf tires - varying topography (hills, ditches, etc.) - don't ever remember having a traction problem.

If you have wet stuff, the machine will sink in,

My ZTR sinks in down by the creek a couple times a year. I either pull it out with my old farm tractor, or sometimes use a come-along chained to a large ash tree.

I think that if a good option for ztrs was lugged tires, the manufacturers would sell some that way.

"I think that if a good option for ztrs was lugged tires, the manufacturers would sell some that way."

Some do, especially the ztr's with the front mount decks. I see more Grasshopper front mounts with chevron lugged tires on the drive wheels than without. See link for a typical setup..

Here is a link that might be useful: Grasshopper ZTR

The turf tires are at the PSI recommended in the manual.

I may check into the lugged tires. My "lawn" sure doesn't look like a golf course so if I scrape a spot because of the more aggressive tires it's no big deal.

The reason I bought the Ferris was because of the suspension. Due to deteriorating back, using my JD lawn tractor unbearable.

You might investigate using an "ATV" type of tire. There's a wide variety of tread choices, more aggressive than turf tires, but not as aggressive as an ag tire. Do a search here or elsewhere, have seen several posts on the subject. You may find a better price on the ATV's as there are so many of them compared to the Ag tires.

Good luck,

Ev