Done it, my best time is about 13 mins.
The fastest route through Bowser's castle are doors 2 and 5.
Plus, Try not to have to redo ANY level for ANY reason, other than SW2 to get Blue Yoshi for SW4.
*My real signature went on strike, said something about "unfair working conditions". So, this is a temporary replacement sig, until I can work things out with the real sig.