I have a tiltable table (using electric actuators). I simply remove the belts by pulling on the rear belt holders (the ones with the screw at the back), fold the belts up and tie them with an elastic band or twist tie, then lift the gantry off the table. Whole thing takes less than a minute, and putting it back on takes about the same.
I store the gantry on a shelf at the base of my table legs.