Proper lag reduction at the start of the level will save about 3-4 lag frames, or two real-time frames. The inputs are C-Right, then Mariocam C-Down & C-Left.
The Tip Top of the Huge Island is the second star of Tiny-Huge Island.
By pressing Z on the first frame Mario is able to walk after clipping up to the top of the mountain, you are able to preserve your speed, saving half a second or more. The speedkick doublejump ending movement can be done whether or not you preserve speed, but if you don't preserve speed then a dive rollout over the edge of the mountain will be approximately as fast.