It isn't possible to do an infinite one since the situation where all the pieces face the same direction happens every time the last one does full circle (or half circle). It would be possible if that situation wasn't forced by author.
I have the same glitch. After i fight the boss and get the msg i have to erase the memory it goes straight back to the dream.
thats annoying because i was so close.
in the "what" (last) level i used a lot of second selves to just go into the hole (sometimes with jumping) and when i got enough i could easily get onto the other side.
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