I think that you could still keep the outlines if you try to avoid using them so much on the inside.
Made an edit here to show you:

I did a few other things too:
- More consistent lighting, more contrast, etc.
- Flattened or otherwise simplified the form (simplifies shading and often helps readability on small sprites)
- Leaned the palette towards a cool blue (helps to both unify the palette and reduce color count)
- Changed the lines a bit to make the silhouette a little more solid (fewer "holes")