How to calculate the forces and moments required to aerodynamically actuate slats?
Very interesting challenge and very interesting design approach.

I've read this had been done few times with TE flaps but not with LE slats. If i were you I would take the following approach to figure a way out. 


In Javafoil you can model open slat multi element air-foil. The results are not very accurate at your Reynolds number if there is a huge separation bubble though. xfoil does not support this feature at the moment but if you are thinking of using TE Flap your best bet is to use xfoil). Calculate several slat gaps by geometrically altering the input file for a list of angles of attack.
You can easily export the local CPx data to a text file in Javafoil. Then use these data to find out how much of aerodynamic force the slat generates by integrating the local surface slope and CPx values for each slat-gap, alpha pair. 
Then this data-set could be interpolated to find out what would be the slat-gap distance for given angle of attack for a given spring constant and substantially to find L/D for each angle of attack.  


Hope this helps.
ABCD

PS: One example of automatic TE flap deflection is discussed here. I think LE slat would be much more effective because $Cp_\alpha$ near the LE is much higher than that of the TE