Red pointer, good visual feedback! (I could also encourage some sound design to help with feedback but you probably already knew that)
I totally understand how removing the triangle in the repeated loop levels would increase the pace. I think it's a nice idea since you have to restart at loop 1 every time.
The triangle is driving the most augmentation to gameplay, however, and removing it for those levels might be give a very samey experience. Like without that triangle I can just scribble in the loop anywhere and there are no consequences or things pushing me along (maybe that's a good thing and intentional) .... BUT if the triangles are gone, we can just speed through it (and have the alternative challenge of avoiding the obstacles at higher speeds with less reaction time.
For the loops that are first time played, though, the way it is now might still give people the same impression. So maybe it's a really nice opportunity for you as a designer tp shake things up (mind you, I have not made it far into the game so apologies if you've already thought about this). You could play with the width/angle/degree of the sector, the speed of rotation, number of loops available (like concentric loops or alt. paths that has the player moving radially as well as rotationally. This lends to varying obstacles/enemy patterns at different radii, and also the speed/length. One could make some other strategic choices such as risk some heart loss for a reward like a powerup, something to make me ignore damage for a time, or an increase in triangle width temporarily or permanently, so I have to make some meaningful choices. Just food for thought.
TL;DR I like the idea of speeding up gameplay but letting people complete previously-completed levels faster for each run-through, but worry about gameplay variety.