The final bit of your puzzle is that, knowing the latitude of alignment, the platform knows the 'earth rate' at that latitude and rotates the platform until the 'east west' axis is requiring that tilt rate to
stay level. To 'de-Greek' that, if your 'east west' axis was intitially north south and you were at the equator, say, it would rapidly get out of level (at 15 deg/hr) as it was being corrected for an earth rate of 15 deg/hr when in fact it was not requiring
any correction when aligned north/south.
Try using two sticks set in a cross, held horizontally, mark them with different coloured tapes and 'rotate' them as if they were earth aligned but with different initial alignment errors. Start at the equator and when you have that sorted, move to the poles.
That even used to work for Lightning pilots.........
Then you can progress to explaining 'strap-down' alignment
