The warpless strat for this level has several interesting tricks. First, the pipe glitch can still be used to warp to directly to the "Tetris" autoscroll room instead of jumping on the bouncy arrow over the save ring, since only 1-1 warps are banned. After loading in on top of the pipe, simply press down and jump on the same frame as illustrated below. This saves between 1-2 seconds, though will cost time if you accidentally re-enter the pipe.
Insane shell jump strat with comparison: 
After the autoscroll, the falling rock section can be skipped by bouncing off of any of the floating shyguys or jumping off any of the floating crates. It is recommended that you find a spot to jump such that you can just hold down forward and jump and the autoflutter will bounce off of one of the flying shyguys. A couple of strats are shown in the following GIFs: