I am trying to subtract the two cylinders from the base mesh (everything is a solid) but it is not working. Is there something you see that might be causing this?

Ok - i've figured out it is only the cylinder on the right side that will not subtract.

Ok so... not a solid as it turns out.

Yes your piece part on the right is not very clean!

Better to redraw it!
Hide the Cylinder
Kill the internal circular face, kill the circles edges, redraw a rectangle face, Join for a solid
Unhide
and make your boolean Diff

Hi Charlie, the problem is an anomaly in the vertical "side wall" area of this hole:



That surface has edges that go all the way around the hole but the underlying surface for that face is only half of the size it is supposed to be:



That looks like some kind of bug but the bug was in some prior step of construction.

I repaired the model by removing that bad face and building a new one and joining it in. The repaired model is attached and should boolean ok now.

If you happen to know how to repeat the steps to get that bad face in it please let me know.

- Michael