In a run, the first save ring should be skipped either by fluttering under, or by performing a first-frame jump on the yellow platform, which launches Yoshi over the save ring. This can also mess around with your timing so be careful when jumping on these 3 platforms, run on them for a brief amount of time before jumping to avoid this problem.
After going up the first pipe, a pipe glitch can be performed, warping Yoshi into the adjacent room. This is faster than taking the arrow lift.
In a single segment run, this level should be entered with as many eggs as possible, as egging the key pot is twice as fast as pushing it.
Fast cloud door shot: