I guess the myth of the supernatural power of V-brakes came from those comparing them with, as you so elegantly put it; " piss-poor centre-pull with prehistoric brake blocks on steel rims." I installed Avid SD7 V-brakes and matching brake levers on a Surly Cross Check that previously had Shimano canti's and the "power" did indeed increase somewhat but certainly not dramatically and only to the point where control was actually better.

I agree the OP should replace those Tektros with Avid or Shimano brakes and enjoy the improvement.