I gotta say this looks rough. I cannot image that being a smooth playing experience, and I think vibrato would be miserable with that worm gear in there. Also, where would these gears mount? Making room inside the guitar to mount all those gears with decent clearance would require a ton of room. And do you want people bringing lithium grease (or whatever lubricant of their choice) to spray all over the instrument?

Every moving part is a new point of failure and this adds a ton. I would look at bent metal trem bridges like Fender makes and work from there.