Not sure why I only just thought of this to solve the shrinkage issue -
Can you over extrude the first 10 layers to compensate for the shrinkage? How about printing the base with "Baffles" to act as a sort of thermal expansion zone for the first few layers?
The less dense the part is printed, the less shrinkage you will see, right?
Measure once, Cut twice, Print 3 times.