In Illustrator, remove any unneeded layer from the document. If you import a bitmap you want to trace, remove that when you're finished.
When you finally have what you want, copy the whole image into a completely new Illustrator document, before saving it as a SVG file. I've noticed that does wonders.
Also helps a lot to simplify a path with 99% accuracy. Takes away a lot of excess points, without influencing the shape of the image too much.
When all else fails, separate the image in layers and upload those one by one. It's a bit of a drag to composite all those layers together again in the Livery editor, but it's a technique that works for more complex images.