I think the idea of rotational grazing under a pivot sounds great. I use a lot of the "slinky" type gates and could see how just opening a few of those as the pivot goes by would not be a big deal especially if the cattle are in a different area when the pivot goes through that fence. If you feed the cross fences from the perimeter fence, opening a slinky gate at the end will also de energize the fence as the pivot goes by.

Rectangular paddocks are better than pie shaped but if pie shaped is easier to get you started and manage with a pivot then I would go for it.  1500 ft to water is not a big deal. However in Fla with no freeze up to worry about 2 waterers would be better than one.

Rotational grazing lets you really up your stocking rate. In fact you need a higher stocking rate to really get the full benefits of a rotational grazing system. 15 head on 8 or 10 acre paddocks of irrigated grass is not really high enough stocking rate for the system to work.

Using a pivot seems like it would overcome the main concern of a rotational grazing/higher stocking rate system: what do you do if it stops raining???  In my non irrigated northern system I am building a stockpile of wrapped hay bales as insurance. However with FL sun and consistent water from irrigation you should be in ideal situation for rotational grazing. jmho. Good luck.

Jim at Dawn