If revving in neutral didn't help, your fan is probably junk. Not enough pitch or not enough blade width. Try a different mechanical fan with more / bigger blades and see what happens. They are cheap enough in the junkyard. I had that happen where the car would boil over when idling or trying to go through the drive-up window line at a restaurant. Pegged the needle at 260°. It ended up my fan just wasn't moving enough air. I put a bigger fan on it (with a fan clutch) and it completely solved the problem.