Hi Sophie, so off the bat after looking at your model I'd say you're running into some problems from some super skinny compressed geometry. When surfaces are compressed down to some really skinny needle like shape it can make a lot of operations that involve complex calculations like surface extensions and intersections to become a lot more difficult to do well.

Your skinny compressed shape starts in this area here:



And then continues down down down to the end like this getting skinnier and skinnier:




It's going to just generally cause problems to have that type of slivery shapes.

Another problem area is a little gap between pieces here:






These areas need to be a bit more crisply defined, like the transition between the pieces would want to be edges that are shaped more like this:





Looking at some of the surfaces involved it looks like you may have ended up with this by cutting 2 pieces that have a lot of shared surface area meaning that the original surface and the cutting surface approached each other and kind of skimmed along each other with a lot of overlapping area rather than meeting at a more sharp and distinct intersection.

Maybe we should go back a few steps and see how just one individual section was formed so that can get tuned up with better quality non-slivery geometry more at the start, once you have things like that in your shape as its main pieces other operations that try to construct things off of them like offsetting will tend to inherit and even exaggerate the problems.

- Michael