There are no significant advance purchase bargains on Japanese trains. It's strictly by mileage plus express surcharge, and since you are not returning to your starting point, there's no advantage to a JR Pass or excursion fare.

In general, if you're staying near Ueno, take the Keisei Skyliner to Keisei Ueno. It's just a short walk from JR Ueno, and the trip is only 40 minutes.

From Ueno take any train on Yamanote Line loop (or a cab, especially if you need to travel at rush hour, which can be brutal on the Yamanote) to Shinagawa. (Tokyo Station would work, too, but Shinagawa is less confusing.) Then take any westbound Shinkansen to Kyoto, and the Haruka Express or a bus from Kyoto to KIX.

That seems to be the least fussy way to do what you want to do. Yes, you could take the Nankai Express from Osaka-Namba, but getting yourself to Namba would add an extra train trip or two.