If you have less "downwash", I suggest you would have less lift, not more, from Newton's second law - less change of downward momentum to the air, less upward force on the wing.
That's where I got to also, but it is less than helpful isn't it
For lift: the speeding of the air behind the wing backwards, when close to the ground, as compared with at height, causes an increases in the flow rate over the wing, greater downwards mass flux, so a greater change of momentum and more lift.
I flirted with that idea, but the problem is that the measured data shows that neither the upper nor lower TE static pressures varies with height above ground at a given AoA. That means (using Bernouilli) that the velocities at the TE are not varying with height either, which sort of puts the mockers on it.