Do you not have an electric guitar available? That's seriously all you need for the biggest part of your project (as you have stated it).I don't have a pickup around to test, and we are being locked down.
You seem to want to get in much deeper than necessary for a perfectly good experiment.
Tension from the machine head is the same as tension due to pressing with your fingers (at least, when using steel strings). It is easy to calculate string tension by applying a measured load (hanging a mass from a horizontal string) and measuring the displacement. You don't need to hang masses from a string hanging over a pulley. (Which is what the pictures of school experiments always show)
The standard of construction of even a modest instrument would be hard for anyone but an accomplished woodworker. Laying out a fretboard well is best done on a proper jig. Any special construction would only le necessary way down the line.