One way to reduce hinge gap is to taper the bottom leading edge of the control surface. The top of the surface should almost touch the trailing edge of the wing, horizontal or vertical stabilizer. Place the hinges as close to the top of the control surface as possible. The surface will move up because there is very little interference. The downward of left/right movement will be limited to the angle of the tapered part of the surface.
Let's see if I can demonstrate on this keyboard. |\ vertical line is the wing or stab, angled line is the taper of the control surface. This has always worked for me, just hope I made it clear.