Emulator used: BizHawk 2.9.1, NESHawk core
Game hash:
Sha1: ACEC431CAB42C1143374499482B0A1332A93AAA0 Md5 : 5870755E1652C3C62BF21C319853FB15
Just the first world done. Lots of trying to be grounded for max speed when possible, usually involving the shorter spin jump or even shorter low jump to get back to being grounded. Entering doors quickly is a matter of releasing left or right for a while. Level 1-2 does a little lag management at the start by tossing the shell at the koopas as otherwise they cause a ton of lag.
Gotta do a check on how the RTA runs play the rest of the game since the cape is helpful but you're not grounded. There might be a few cases where not flying over the level might actually be faster due to faster grounded movement.