The list of requirements don't really match the budget. Closest is probably Logitech G703 LIGHTSPEED which is $60+/- with warehouse deals.

Perhaps I'm overlooking some options due to a lack of familiarity with which brands have good Mac compatibility, but out of the relatively few options for large wireless palm grip mice, the ones I can think of are at least $60 with warehouse deals.

If Steelseries mice work well on Mac, then the Prime Wireless can be had for $40 but it's closer to medium size than large.