What we usually did was remove the second stage and machine the gearbox casing to account for the different height, but your solution seemed clever, so we came up with this:
We machined the aluminum spacer (3mm, ~1/8") on our home-made CNC mill, but just because we're lazy - that part could've easily been made with simple tools. The hole is somewhat smaller than the gear's outside diameter so it gives a pretty tight press fit (squeezed the harder steel and aluminum together in the vise so that the spacer deforms into the shape of the gear).
Thanks for sharing this and we hope our solution helps someone.