I don't quite understand how the faster you are up to corner velocity, the tighter the turn?
Because the turn radius doesn't just depend on speed, it also depends on the radial G. At lower speed a greater proportion of the total lift being generated by the wings is needed to counteract gravity so that the aircraft can maintain the horizontal turn, so less is available for turning. In effect the pilot needs to reduce the bank angle as the speed drops in order to keep the aircraft in the air, so less lift is being used to turn and consequently the turn widens.
As your aircraft gets faster the reverse process occurs. As the speed increases, the total lift increases and so a smaller proportion of it is needed to maintain horizontal flight. The bank angle can therefore be increased so the radial G doing the turning will be a greater proportion of the total lift, so even though the speed is greater the turn will tighten. This will continue all the way up to the G limit, and so the tightest turn will occur at corner.
The catch is that the maximum coefficient of lift for an aircraft isn't really constant, it is influenced by Reynolds and Mach effects and so things are a tad more complicated, particularly as the speed and altitude range for fighters increases. When those factors are taken into account for modern fighters it is possible to see EM diagrams where the best turn radius occurs at corner under certain conditions but where it doesn't occur at corner under other conditions. All you really need is a full set of EM diagrams.
That's the simple explanation, and the good news is that real WWII fighters had a much smaller operating range and the best turn radius in a horizontal turn was at corner.
Hope that helps...
Badboy