If you look on a map, the Osaka Hyatt is in a really crappy location. It isn't particularly closer to KIX than anything else in Osaka, and it is really far from most of what you would want to see in Osaka. If I were in your shoes, I would forget about using points, and try to find a decently-priced hotel near either Umeda or Namba. The best day-in-Osaka itinerary (IMO) is to walk from Umeda to Namba or vice versa, roughly along the Midosuji (the main north-south avenue, also the route of the red subway line), and check out stuff along the way. They both have direct train access to KIX, and if you are in Umeda you also have a straight shot by train to Koshien.

Staying in Ishiyama for three nights sounds like the pits. I looked up that hotel and it is right next to an enormous Toray factory. Is there really nothing in Kyoto that you can afford?

If you have time in Tokyo and like baseball (as it seems like you do!) you should also try to catch a Swallows home game at Jingu Stadium (near Omotesando). It's an outdoor ballpark and has a much more small-town feel than Tokyo Dome, and the Swallows fans are a riot with their umbrella dance after each run.