Suggested workflow for vectorizing logos with gradients

I was impressed with how much grunt work can be handled within AI’s image trace function:

Object -> image trace -> make and expand

However, for more sophisticated logos, things become less straight forward. Consider a logo like this:

In this case, image trace clips off the lighter portions of the logo. I’ve only found two (slightly drudge-laden) workarounds:

• Flatten the highlights to make a more mono-tone look (then need to
  apply own gradient afterwards)
• Retrace by drawing lines and joining (but this only looks
  professional with squares and the like, circular elements are hard to
  ensure exact proportions — at least for me)

Question

Are there more refined approaches for this kind of task? Or feel free to add or improve upon my ideas mentioned above.