The coverage map for Intelsat 707 is deceiving. The edge of the footprint has an EIRP of 32.3 dBW, for which Lyngsat recommends a 10' dish. However Florida is not on the edge of the footprint and almost certainly receives more power than the edge. Unfortunately the coverage map provides no other contours. The beam peak is shown as 40 dBW, which is pretty typical for C-band. It's hard to say with any certainty, but I expect an 8' would work fine and there's a decent possibility you could get by with a 6'.
HOWEVER, Intelsat 707 is a circularly polarized satellite, which is untypical for North America. While a number of feeds can be adapted to receive this type of transmission by inserting a dielectric plate, all but one will then lose the ability to receive linear polarization, which you need for Intelsat 1R. Also there are significant CNR losses caused by these plates, which might force you to a larger dish. There is one feed that doesn't suffer from these losses, but it's very expensive and it cannot switch between circular and linear without a manual rotation.
I'm not sure SportsMax is still there. The Lyngsat listing for it dates to 2005 and when I looked a month or so ago, I saw no hint of it on the spectrum analyzer. However I'm in Colorado so I may be out of footprint if that happens to be a low power transponder or if this is on a Caribbean beam. I wouldn't proceed with Intelsat 707 until someone chimes in that this feed is still there.
I'd recommend a dish with an actuator rather than trying to space the feeds 8 degrees apart. There is a lot more up there worth watching than just these two birds. If you try to mount two feeds on the dish, because of the problems of getting circular and linear polarizations on the the same feed, you'll generally do better by offsetting them by the same amount. For example, if you mount one feed dead on-center and the other 8 degrees off-center, the latter will suffer around a 3 dB loss. On a 8' dish, that will give only a sensitivity of a 5.7' dish. If both feeds are offset by 4 degrees each, you might only suffer about a 0.75 dB loss on each. I wrote a thread on how to get this down a lot more, and in that case I couldn't measure any loss at all.