FINALLY, I got a S rank (without trinkets) for SS2! I made it on 2:11. 6 seconds from my "forum record" previously made in 1.2. ...
...Not really. Because of
this glitch, 2:11 might be equal to 2:13 on 1.2 and 2:05 might be equal to 2:03 in 2.x. It isn't a good idea to compare times made in 2.0. or 2.1.beta with ones made 1.2. ... Also if 2.1. (stable) ever gets released with this fixed, then it wouldn't be a good idea comparing times made in 2.1 (stable) with ones made in 2.0. or 2.1.beta.
Here's what I'm going to do:
Try to get S ranks without trinkets as fast as possible, specially in the Lab and SS1 (one of my shortcuts in SS1 doesn't seem to be possible to make?!),
Try to get V rank in the Final Level,
Try to get V rank in the Lab.
Oh hey I beat No Death Mode.
Pretty fun challenge. As others have said, the Gravitron is by far the most difficult part of the run - although I think the second half of the final stage comes close. Miraculously I got this success on the first time I reached the difficult part of the final stage, so it's all good.
Maybe I'll check out some of the custom levels now.
Congratulations! As far as I know, this is the 2nd time someone made a video of beating No Death Mode. I was also amazed how fast you were, that I thought the video was fast-motion (understand?). However, when I skipped to the final part, I realized that I was wrong as the time showed was almost the same as the time of the video. 18 minutes?!?!

That's very fast!
Are you going to try beating No Death Mode, collecting all the trinkets?
EDIT: Okay, perhaps 18 minutes isn't very fast, but still fast.