I wanted to call this "How I mastered the elevators", but I'd be kidding myself. Still, I'm clearly on the right track now.
First I researched how to play the board; the most helpful has been
this video. Then I used
my "Loop current stage" cheat together with the "Infinite Lives" cheat to make sure I stay on the elevator board. Then I challenged myself to beat the board ten times in a row without dying. I would keep playing until either I hit ten or I was too tired or aggravated to continue. If I did hit ten, I kept going until I died to see how far I could get.
If I cleared the board but I felt I did not do it properly -- that is, if I was not properly watching the springs and I just got lucky -- I did not advance the count, but I did not reset it, either. If I was not entirely sure I was watching properly, I gave myself the benefit of the doubt and awarded myself the point. Any time I died, though, I reset the count regardless of the reason, even if it had nothing to do with the springs. After all, in a real game, the game doesn't care how you died, merely that you did. Currently my best score is 20, which would be enough to reach the kill screen, provided that I play the other boards perfectly (spoiler: I can't). But I can't pull off 20 or even 10 in a row every time yet.
I noticed that there seems to be more than one right way to handle the second safe spot. You might put Mario in the rightmost area of the safe spot, then when you make your dash, pause at the ladder while watching the incoming spring. I didn't have very much success with this, so I started moving Mario further to the left so I wouldn't have to pause at the ladder. The best spot for me seems to be to the right of the center of the elevator, so that his hind foot (when facing right with both feet on the ground) is over the little circular hole in the elevator and his front foot is at, but not over, the edge of the elevator. Maybe the right spot for you is different. If what you're doing isn't working, don't be afraid to experiment! But do note that when you change up Mario's position like this, it may be a little difficult to adjust; you might keep missing the ladder and having to run back and try again. Give it a little time and you'll iron that out.
Oh, and a little tip: each time I cleared the board, I said the current count out loud. That makes it easier to remember the count, because hearing the number uses different parts of your brain than merely thinking it.
