Perhaps even worse, PCBs also have hysteresis. That is, as you go around a cycle on the stress-strain curve, you don't end up where you started. It takes a set. There's also some creep (time-dependent strain response), which we're more familiar with as making bolted PCB connections unreliable.
A more mundane solution might be preferred -- for example a spring with a deflection meter. Which could perhaps be as simple as a mirror, LED and photosensor -- it won't be linear or anything, but given a series of calibration loads, you'll get an idea of what you're measuring. (Some flex resistors might be okay, but it's actually not great to use turn or slide pots -- they have a lot of stiction, causing blacklash in the measurement.)
Or a magnetic solution, using a solenoid or electromagnet of some sort to maintain the counterforce. Now, this can be a bit tricky: normally, the magnetic force varies something crazy like the inverse cube of displacement. That makes measuring a displacement just about impossible, but if a displacement sensor is combined with it, servoed to maintain it at some balance point -- now only the gain of the sensor matters, not its linearity (aside from locally), nor the magnet's. Held at a constant position this way, the magnet applies a force proportional to current (up to a limit determined by size and construction -- magnetic saturation), so can be sensed very accurately.
Bonus, such a rig can be turned upside down to levitate objects hanging down from the magnet.
Alternately... get one of those levitator thingies and try to beef it up?
But yeah at this point just buying a strain gauge is looking pretty nice, I'll admit.
Tim