How would one calculate the thrust-to-weight ratio for a minimum turn radius?
You can't. Turn radius is a function of true airspeed &amp; bank angle, and nothing else. A J-3 Cub flying at 40 knots will have a pretty tight turn radius compared to an F-16 with its 9-G turn at 100+ knots, just because the Viper can't approach the Cub's low speed. Or take a KC-135R -- better T/W than a T-38, but not really a low-speed performer nor a high-G machine.

Turn radius in isolation will favor low-speed aircraft over high-speed aircraft, even when the latter have better T:W ratios.