My delete nightmare

The spirals on the inside of the tube need to be deleted leaving just the spirals on the outside intact.

The tube is a group and the spiral ‘bracelet’ is a component. I select the spiral and ‘intersect with model’ so in theory I should be able to select only the elements of the spiral on the inside of the tube and delete them. But when I select those unwanted inside elements, surfaces of the spiral on the outside of the tube which are connected with selected surfaces on the inside the spiral also are selected. If I delete them this happens:

Please help me kill the unwanted guests!

I suspect that the facets in the ‘spiral’ form are quite tiny.
If operations like Intersect result in edges less than 1/1000" long they are not formed.
So subsequent deletion-tidying can erase parts unexpectedly.

Make the parts various parts into a component.
Copy it to one side and scale that copy x1000.
Edit the copy and do the intersect.
You should now get all of the cut edges forming.
Delete the unwanted parts.
Exit the edit-mode.
Delete the giant copy.
Now the smaller version should show the tiny geometry OK.
Tiny geometry can exist, but it cannot be ‘created’ from scratch…