[subliminalzen]

If multiple software companies have successfully trademarked the exact same single word, does that matter or not? (They're all sharing it already.)

Yes. As someone who owns a trademark, I can tell you it does matter. Pick a new name.

I would guess that all of these matter by degree, and potential trouble only depends on an adversary's willingness to litigate, but am hoping for some help or guidance in what is a complicated (and frustrating) aspect of our business.

Trademark owners must defend their trademarks against infringement. Expect litigation, every time.