RE: Need thick laminar flow airfoil with rounded trailing edge
How fast do you plan to fly this wing (what Reynolds number)? Can you make it with a cambered airfoil? You haven't provided enough info . I believe it won't be a problem finding an airfoil that produces L/D of 10 that fits the criteria you stated - 4' chord and 1" TE radius. If the flight speed is very slow it may be more difficult.