I was thinking of some slightly more "wacky" options to get from KIX to Tokushima - and came up with:

(1) Wacky Option 1
Ferry from KIX to Awaji island. Then express bus or rental car to Tokushima.
(There are no major car rental companies on Awaji Is. but I found a couple of local rental companies)
- Depending on your arrival time at KIX, you might choose to spend a night on Awaji. There are a couple of spa hotels near the ferry terminal, which look pretty good online. (I regret I don't have first hand knowledge of them).

(2) Wacky Option 2
Nankai railway from KIX to Wakayama Harbour (Japanese = "Wakayama Ko")
(Fairly simple train journey - take the Nankai line to Izumi sano (a few minutes from the airport) annd change trains there to the line that goes South to Wakayama Ko).
Then take a ferry from Wakayama Harbour to Tokushima Harbour (2 hours)
http://www.nankai-ferry.co.jp/timetable/index.html
(Tokushima harbour is 15 mins by bus or taxi to downtown Tokushima)

EDITED TO ADD: On further examination, the second option looks very good. Not wacky at all.... The train + ferry will take roughly the same time as if you took a limousine bus from KIX to Tokushima. The schedule seems to work for just about any arrival time at KIX - and so long as the weather is OK, the ferry would probably be more comfortable than a cramped bus seat.