How to calculate the radius of a turn as a function of speed, bank, wing-loading, and Cl?
The formula for turn radius is Velocity squared divided by radial G. And since Radial G, (assuming a level turn) is absolutely dependent on bank angle, the turn radius IS absolutely dependent on Velocity and bank angle. No other factors are necessary.
You are incorrect that two aircraft with different wing loading will have different turn radii at the same airspeed and bank angle. Anyone who has flown formation, even if they are not familiar with the physics/mathematics involved, knows this from experience.