If your volume is low, i would agree with the 2 pcb approach, make your main PCB to the thickness of the fingers. copy the project so all your holes are aligned. and make a second for the remaining thickness, specifying no soldermask on the 2 surfaces to be joined, you would then glue these 2 together,
For middle volume, same deal, but you could likely get them hot pressed together still at the factory, as its not too different to how buried via boards end up being built.