Thanks all. So I dug around on the internet, it looks like the plant (mostly) there (and lots of other places too) now is called Japanese grass. Annoying, pervasive, and hard to get rid of, but not dreadful and doesn't (I don't think) require horrible toxins to kill -- however, in case it's not already apparent, we're pretty laissez-faire (understatement) and this grass really is all over the place in our area. I'm game to do stuff that reduces its prevalence in the yard (rocks, mulch), but not likely to put in the effort to get rid of all of it (yes, I realize that means this will be an ongoing issue -- but it probably would anyway, as it's also in lots surrounding ours, and, again, we've survived ~2 decades together, what are a few more?).
The rock garden/Japanese garden suggestions are good ones, I'll look into those. Thanks for the native plant links! And fair point on the stream -- I'm not intending (or wanting) to do anything to it that would alter its flow or pollute it, and given its tiny size and our rural-ish location, the likelihood of anyone even noticing that I've made any changes at all are slim, so I don't think that's a concern.
On a positive note, no pine branches causing problems -- these are big, big pines (100' plus) and the branches are way up high.