you cant float ac. you did a nice job of changing ground points but floating is a dc thing. the 2nd poster is off a little bit. no problem running 12v, that's exactly why you changed ground points. auto leds will work. no need for 4.5v.
on the 2nd posters talk about blinky bike stuff that runs off 4.5v its easy. cut out the blinky board and run a emitter follower voltage regulator at 4v. the led's last forever when you lower the voltage slightly. I know its over everyones head but it costs less than a buck and works flawlessly