lonely: Yeah, I know about Drill Rush's little jump at the end. In fact, that's why I didn't mention it above: I may well have experienced this phenomenon with Drill Rush in addition to Meta's specials, but I've not paid close enough attention to be absolutely sure that it wasn't the innate hop that comes with the move. I'm absolutely certain that I've done it with his other three specials, though.
UltiMario: With the way that the last few frames of Dimensional Cape are animated, it can, on occasion, look like a jump. What I'm experiencing, however, is different: Meta goes into FallSpecial (I believe it's called that, at least... I just mean the animation where you're falling and can only move left/right a little bit), stays in it, and does a little hopping motion while staying in FallSpecial--not changing his look at all, just kind of popping up a little bit. It's rather odd.
Lgnd: DR doesn't hop if you drill into the ground, IIRC. I could be wrong, but don't think I am. I've heard of cancelling Shuttle Loop before the glide, but never really tried it, so I can't comment. And... while Dimensional Cape may seem similar to Zelda's Farore's Wind at first glance, it shares much more in common with Pika's Agility (or was it Quick Attack?) in that you can move it in two independent directions while invisible. Personally, I use this to counter the main problem with the move--the lack of a long period of invincibility. If you teleport up-right and then down-right, for example, you get the same or more horizontal distance than you would from just going right, and you won't get hit from the front when they attack where you "should" be. This allows fast f-tilts from behind with little chance of punishment, as long as your timing and aim are both semi-decent.
I'll try and come back later today, but I have a monster of a research paper to write before the clock strikes twelve. Hope we can reach some breakthroughs in this field of study!
(Forgive spelling/grammar errors, please... I'm on my phone, so I lack spell-check and such things of that nature.)