Oh I see, very different than what I first envisioned with initial description.
You have a lot of delicate members between the cut-outs IMO. Another consideration is how those bridges will survive the bumping around in the tumbler. I've heard most of the issues people deal with are parts hitting one another as they likely to contact many times. This is less of an issue for small parts because they have low mass & smaller volume so more media between them & less momentum when they contact. Also I think the media might be sized not only on abrasive/finish issues but considering what might get stuck in the nooks & crannies. But leave that to the finishing company to guide you.
BTW are those laser cut?
Are you just embarking on choosing a metal finisher or you have exhausted some options already & casting the net out further?