I am basically trying to determine the change in lift, drag, side force, roll moment etc when the aircraft is in ground effect compared to out of ground effect.
There is no way to do this in a reliable manner without conducting a flight test measurement campaign.
You can find rule of thumb formulas in books, such as Roskam's "Airplane Aerodynamics and Performance", but they will never be very accurate.
In Roskam there is a reference to "Fundamentals of Aircraft Design" from Nicolai as the source of a diagram linking $A/A_{eff}$ to $2h/b$, but no explicit equation is given.
Roskam provides the following equation for the change in effective angle of attack:
$$\Delta \alpha_0 = \frac{t}{c} \left( -0.1177\frac{1}{(h/c)^2} +3.5655 \frac{1}{(h/c)} \right) $$
Then, applying this equation they derive the change in lift coefficient:
$$C_{L_g} = C_L \frac{C_{L_{\alpha_g}}}{C_{L_\alpha}} - C_{L_{\alpha_g}}\Delta \alpha_{0_g}$$
For induced drag the following equation is offered
$$\Delta C_{D_{i_g}} = -\sigma' \frac{C_L^2}{\pi_A}$$
with
$$\sigma' = \frac{1 - 1.32(h/b)}{1.05 + 7.4(h/b)}$$
"Wing resistance near the ground" from Wieselberger, aka NACA TM 77 is cited as reference.
No other formula is provided.
Having tried to use this in the past, I would like to stress that these might be useful to get a feeling for the quality of the changes, but they are absolutely not a sufficient substitute for proper modelling or in-flight measurements to get a representative quantitative behaviour.