Lemurian,
The only way I can see a coefficient of 600 in Mach giving anything close to the correct KTAS value is by including a coefficient for the temperature term.
Regressing KTAS asgainst M and M*(T+35) values yields:
KTAS ≈ M[600+1.22(T+35)], (T in centigrade)
The error within the range I've checked (0.5 ≤ M ≤ 0.85, -75 c ≤ T ≤ + 45 c) stays reasonably small, < |2.3|. The maximum positive error (KTAS minus the approximation) won't exceed 1.44 KTAS over this range.
The +35 c tweak to the temperature was necessary to force the coefficient to a friendly 600.
Calibration and validation of model available on request.