Some runs:
Failed World 3-Castle 100% TAS (0.9.8)
I was inspired by your post to make this, ais523! (I think the trick has been fairly known (mindnomad and I have known, at least), but I'm not completely sure.)
You can keep the invincibility state by simply ducking for 2 frames after full speed and repeatedly jumping.
I can't find a good way past that last pillar without taking damage. Luck does not seem to affect it, nor does screen scrolling... but I suppose taking damage won't waste too much time, anyway.
World 2-1 100% TAS (0.9.8)
Shortly after I made that TAS, mindnomad encouraged me to make this one. It looks pretty nice, I think.
World 1-2: 1-frame improvement to the any% TAS (0.9.7)
It seems that while at a near halt, you can gain speed faster with the Blue Shell by ducking and holding in the opposite direction you want to move. (I remember coming across this when trying the beginning of 8-3 before but couldn't find another way to utilize it.)
(Hmm, there still doesn't seem to be enough improvements for us to work on a new run, though; sorry! :( )
Although it's already been a while, I'm not quite sure if we're really ready to start the 100% TAS... We may need to find an easier way to know what will happen on the map portions whenever we manipulate luck.
Edit: Oh, and also, a YouTube user named pyigyli made a "no powerups" TAS, if anyone's interested:
http://www.youtube.com/watch?v=fdthW4UIV_M