How can I build a shuffleboard surface that is movable?
Have a look at this link:

http://www.model-railroad-infoguy.com/modular.html

They build modular model railroad tables - and I'm thinking that's kind of what you're looking for.  

I would want a design made up of two or three separate table bases, each of which can be independently leveled at each leg.  When perfectly level, your top surface, something like a high gloss butcherblock top I guss - should line up perfectly evenly.

You'll want some kind of tension latches connecting each section to its neighbors as well, to pull the surface together good and tight once its assembled, to eliminate the seam.

For building techniques, I'd build the bases and top surface separately at first.  The bases can be separate, but the top should be built in one solid piece.  I wouldn't do the gloss coat yet though - I'd build the top and then cut it into two/three interlocking segments and mount them on their respective bases, ensuring they can close up tight to give a nearly perfect surface.  Then and only then would I separate the sections and do the finish treatments on each.