I concur with Whistlestop's advice. I don't think locking tuners will help with that problem.
One test you should always do on an acoustic guitar you are contemplating buying is to string it up with your preferred gauge of strings, bring them up to concert pitch and then totally detune them all except for the top E. If the E string has gone sharp by more than a semitone (I can only speak here for medium gauge strings .012 - .056 ) then IMHO there is too much slack in the construction of the guitar, most likely in the neck but conceivably in the top. Whatever, it means too much energy is being dissipated somewhere, and detuning one string will result in a disproportionate sharpening of the others.
Why don't you do that test on your guitar, Shouter, and let us know how much the E string sharpens by?