The X-Foil program models airfoils to produce data similar to that obtained in a windtunnel. Mark Drela has arranged with MIT to make this program available to us modelers. At model reynolds numbers it is a lot more convenient than building a model of the airfoil and testing it in the windtunnel. X-Foil for Windows is available as a free download at:
http://www.charlesriverrc.org/

AFSalmon:

You can test your maximum thickness location hypothesis against your choice of specific airfoils with X-Foil. I'll let you do the work. My intuition is that for symmetrical airfoils more than about 12 % thick and with blunt leading edges, the location of maximum thickness less than 30% of the chord results in a very abrupt stall. Such airfoils can have a straight line coefficient of lift vs. angle of attack characteristic. Airfoils like the R140 with a small leading edge radius and a maximum thickness aft of 30% of the chord may not have a straightline relationship between coefficient of lift and angle of attack.