The definition mentioned about the Excelsior was incorrect. It was not stated to be able to achieve any speed. The ship's helmsman said that all speeds were available through transwarp drive meaning that all speeds within the ship's performance envelope were available.
If you actually watched that scene in Star Trek III, as the Helmsman was talking, there was a screen shown that displayed a bunch of numbers which apparently depicted warp-factors. Regardless the numbers (some going over a hundred, and not in order) are probably not all that accurate and the screen shouldn't be taken with too much seriousness other than to show that the ship's warp speed was not unlimited.
For the most part it would seem that Transwarp drive as stated in ST:III, was more or less warp drive in excess of current warp-technology.
Captain Styles in Star Trek 3 stated that he was looking forward to breaking the Enterprise's speed-records. Considering the fastest speed the Enterprise ever achieved was Warp 14.666, it would be logical to conclude the Excelsior was capable of exceeding that speed.
There was a DC Comic strip which took place during the TWOK-TVH Era which dealt with the mirror-universe and it had the ship doing around Warp 15 to Warp 20.
CuttingEdge100