I do not think it will rotate a full 90 degrees in the fingertip. In other locations, like P0 fascia tissue, this might be possible.. but the fingertips are made of different stuff. I don’t think it’s a good idea to try to force or manipulate it to move that way either.
As for popping it out, that’s up to you. I don’t think it’s a good idea but if you want to just abandon this experiment now and pop it out, be clean about it.. wash hands.. liberally use isopropyl alcohol to keep everything saturated while working it out. Cover the wound properly afterwards etc.