Hi Don,

Normally I would use each surface to trim the other, so that will give a good result for joining. Having a quick look at your model there appears to be a slight problem with broken edges.

If you look at the area highlighted(I have removed the cover in this pic)




You will see where edges do not join, also on this side shown, there is an extra little face.




Trying to use that edge directly for trimming can give further problems. So what I suggest, is to select all the edges around that opening(make sure you select them all, as there are 2 little edges(one each side) near to where I highlighted the problem edges)




Once selected, use "Extrude"(with option:- both sides) and extrude that edge into a surface




You can then use the extruded surface to trim the cover.





- Steve


edit.
Sorry, for some reason I made my reply to Bob.