Stand on the first block space on the levitating platform and run right when the third last light post hits the edge of the screen.

After entering the pipe run right and jump off the first note block and perform 3 twirls to reach the next pipe.

After that hold neutral then run right just before Mario lands on the POW block, then precisely enter the door.

Once through, while running right perform a P Switch jump off of the P Switch and land precisely to enter the door as quickly as possible.

Next make your way to the cloud platforms. You want to stand on the first cloud in the line of three that are on the right. When the first line of Bullet Bill Blasters touch the edge of the screen run right and enter the pipe.

Once through stand below the third arrow's longest vertical line of coins and run right when the second arrow's longest vertical line of coins touch the edge of the screen. Enter the pipe.

I finally successfully recorded a full run of this strategy. The video is below.