Hi Bob, I'm glad MoI is working out for you!

One of the difficulties with this particular model here is the pieces you are trying to cut have their ends bent in a sharp fishhook like shape such that they are basically folded back over top of themselves at their ends, it's difficult to see unless zoomed in pretty closely:





That kind of thing with a surface very sharply turning and folding back on itself (so that it's basically "self intersecting") will tend to cause a lot of problems in surface/surface intersection calculations so you will probably need to throw out those current pieces and re-extrude some from a more simplified and non-folded base curve before they'd be usable.

Then for some strategy on how to approach it - the easiest way to do this kind of thing would be to use solids for the pieces and then there's a new feature in the booleans for v3 where you can do a boolean union with some face sub-objects selected and that will make the boolean done with intersections only happening on those selected faces. There's some discussion of this here which several visual examples which should hopefully help explain it:
http://moi3d.com/forum/index.php?webtag=MOI&msg=6663.1

For a case like you want, if you have 3 solids set up like this, with the 2 thin pieces just sticking out some distance past the back, top and bottom of the thickened base piece (again all 3 objects here are solids):


Then to set up the selection, you select the 2 thin pieces as entire objects, but make a face sub-object selection on the main body piece, with just the 2 inside faces selected, so the selection looks like this (2 full objects and 2 face sub-objects are all selected):




With the selection set up in that way the boolean will only cut things using those selected faces, and so when you then run Boolean Union, you will get this as the result from the boolean:



Basically by making the selection of the inside faces you're telling the boolean to temporarily pretend that the object is super thick and it only tries to cut things using those inside faces.

It's very convenient compared to working with just a bunch of individual surfaces. In order to use this you would want to have all the objects be set up as solids and not just as some individual surfaces. I've attached the example 3DM file so you can see how the objects are structured.

Hope that helps!

- Michael