Hi Phil, well it makes things very difficult for the booleans when you have pieces that have overlapping surface areas where the parts kind of barely skim over top of each other which you have a lot of here... Intersection calculations between such things can easily have meandering intersection curves, and for the booleans to work properly the intersection curves need to define clean closed loops so it can divide things into different regions. If you take a look at the intersection curves created in your case here by selecting the 2 objects and running Construct > Curve > Isect you can see that the intersections are very complex.

Some things that I would try would be to make your simpler part to be a large filled block rather than a thin piece in order to avoid some of the skimming and if that's not successful then maybe it will be necessary to work at a surface level using Edit > Trim to cut up things rather than booleans. I'll try some of these things tomorrow to see if I can help you.

- Michael