You can't just "float over" to another point along your orbit; to move the forward Legrange point you would have to slow down, causing you to drop into a lower orbit which moves around the sun quicker, then speed up to a larger orbit that intersects with the desired Lagrange point and then finally speed up again when you reach that point to stabilize the orbit.
To try this in Kerbal space Program: place two craft into the same equatorial orbit, but with one 1/6th of an orbit ahead of the other. Now make them dock.
It's both counter intuitive and easy once you know how.
If you accelerate by 1MPH you're not in the same orbit anymore. It's not like driving on earth, where you can go faster along the same path by pushing the accelerator down; the speed you're moving at is a component of your orbit.
To try this in Kerbal space Program: place two craft into the same equatorial orbit, but with one 1/6th of an orbit ahead of the other. Now make them dock.
It's both counter intuitive and easy once you know how.