Where I live we have extensive hills. One thing that turned me a bit off to the ZTR concept was, in fact, their performance on very steep hills. ZTR's are generally wide in back and have a tremendously rear-favoring weight distribution. Thusly, they perform well on hills that are reasonable. Unfortunately, when the hillside is wet or very steep they can seem like they are doing well then suddenly let go. I have had this happen two or three times in my ZTR mowing career and it is frightening. My experience with the type mowing I do is that a very efficient tractor, like an X series JD for example, will mow at a comparable pace to a ZTR unless the plot is obstacle laden. I have been able to reproduce these results time and again over the years on hilly properties I mow. True, the ZTR is faster but not that much faster. As a result, many of the professional mowers here use X series or equivalent tractors for mowing or they invest in a front cut. Unfortunately, front cut JD's are extremely expensive and have a pitiful resale value due to competition from ZTR's over the years. JD still makes them, and there must be a reason for that. I would say using both a ZTR and a front cut (never owned but used the latter) the front cut is a Cadillac to operate. Super smooth riding and cuts great. Maybe our OP could find one of those.
John M