Oh, wow you are a life saver! Indeed there is a bug in the underground level after you get the cross! I will fix it ASAP.
I assume that by "moving ghosts" you mean the white ghosts. Yes they can get tough, so you have to time your jumps. Thanks!
Edit: I fixed it, although I couldn't replicate the double music glitch. I assume that the cross-dissapearing glitch occurred when you tried to exit the watery caves, and not when you entered the well.