I use a digital level. To make sure that it's lined up right, I have a short piece of PVC pipe that I put across the tops of the slings. Then the level has a flat surface to rest against. You can also turn the digital level 90 degrees to measure slope. (I might laser cut something prettier than my plain old pipe.)

When I adjust things I always wiggle the game like I was nudging it and see where it settles before making any more changes.

Yeah, if you could set the disc into something with square sides then it would be easy to line it up flush with another straight edge.

Your angled shim for the disc is a good idea... I was actually thinking about that the other day. But I am a laser cutter guy, not a 3d printer guy, so it's not quite as elegant for me to make a precise wedge shape. Once you post your design I'll get a buddy to print one for me!

That looks great Anony !