Uniting Vector Draw shapes in Illustrator

Hi there,

This is a drawing made in Vector Draw and sent to Illustrator. It is one piece of a much larger, layered drawing.

Because I am making complex images I would like to simply the paths and shapes without compromising details, so that my file doesn't get too large and unwieldy. (I have found that the Simplify tool changes the details too much).

In theory, I should be able to merge these shapes using the unite tool, however I end up with a distorted result. Here are the steps I've taken with screenshots. (The same result occurs using the Shape Building Tool.)

I'm not good with Illustrator, so any advice on how I can merge these shapes, is helpful 🙂 Thanks!