Nice idea but the requirement for the device is to receive an egg which has been boiled for some unknown time and make a determination.
You’re no fun.
I suspect the neatest idea is the device that takes the egg and gauges the stiffness of the insides by rotating it back and forth. Getting the first few moments would likely characterise the internals well enough.
If a cooked egg spins like a solid and a raw egg barely spins at all, a partially cooked egg must spin in some intermediate way. So study how 1 minute eggs spin, then 2 minute eggs all the way up to, say, 15 minute eggs and interpolate. Then build a device that attempts to spin the egg and measure the response. Shouldn’t be that hard.