You say “number of nodes”, what do you mean?
If you mean the node counts are the same in each of your two original shapes, that’s good.
If you haven’t tried it yet I’d add nodes, especially on your curve segments. The simplest thing would be to select both original shapes, enter the node editor, select all nodes and then hit the add node button twice. You’ll end up with 4x the original node count, and if the two shapes originally had the same number of nodes they should still match. (At 28 nodes each)
The idea is that your paths will be more explicitly constrained and so interpolate should have less guesswork to do.
I’m suggesting this because I had similar issues with inaccuracy in stroke to path, particularly with large curve segments. Adding nodes greatly improved results.
You can see it illustrated here:
If you meant that you already tried adding nodes, well then I don’t have any more ideas at the moment.