Slats and how they work
OK, starting with how slats work aerodynamically.
First of all slats do not increase lift. In fact, if you were to deploy slats and change nothing else you would normally lose a small amount of lift.
What slats actually do is delay the onset of the stall, and that enables you to fly the aircraft at a higher angle of attack, which generates more lift. But the lift comes from the angle of attack increase.
Slats delay the stall by, in simple terms, re-energising the flow on the upper surface. A wing stalls when the adverse pressure gradient becomes too large for flow to continue to move against that gradient (which is of course on the upper surface). The flow starts to separate from the wing, since it's easier to move away from the wing than to keep fighting the pressure gradient.
The flow area which is affected first is the boundary layer, because that portion of the flow is the slowest, and has the least energy to use to overcome the gradient.
Slats (and many other stall delaying devices) help to renergise the flow by providing a 'leading edge' which is further back on the wing (so the boundary layer growth starts further back on the chord) and by providsing highly energised air moving through the slat gap, which helps to energise the boundary layer. (Boundary layer blowing works in a similar way).
As to the mechanical operation of your slats, I'd have to see the geometry. I'm surprised you say they are held out by springs (at low speed), and the airflow at higher speeds pushes them back.
A more typical installation (e.g. Me109) would be to hold the slats IN with springs, and rely on the leading edge suction which develops as you slow down to pull the slats out. But it rather depends on the wing geometry (to know how the suction behaves) and the mechanical geometry (to see how the various forces act).
Hope that helps.