Hook's law and Young's modulus are only ever guides and approximations. For example the extension of a spring depending on the weight applied to it is never truly linear as Hook's law denotes. As the spring stretches it characteristics are altered in a very subtle complex way.
I worked for a company many years ago who sold weighing machine that used a vibrating wire, similar to a guitar string that had a magnetic pick up below it. The frequency then could be related to the weight being carried on the scale. The electronics always had to be tweaked to compensate for the non linear characteristics of weight to frequency that where observed.
With regard to having to constantly re-tension the guitar string for a time until it, somehow, settles down is not so surprising. The manufacturing process is establishing all sorts of stresses with the structure of the wire and over time these will want to normalise themselves. In some manufacturing process this can be speeded up by heat treatment, other use time to do this. Years ago manufactures of machine castings used to age their casting out doors for a few years to let them 'rest', this gave a much more stable casting and hence a consistently accurate machine.
I would suggest some experimentation and pre tension the strings you are using until they are ready to be used.
I hope this may help Brian