So, as an update on this, it somehow appears that it somehow was the old travis-ci.org webhook somehow still installed on my fork, that was somehow causing duplicate CI job checks on upstream PRs created from my fork. Somehow!*
The upstream admin checked all of the suggested settings and found nothing amiss, so nothing was changed there, but since I’ve deleted that webhook the issue hasn’t recurred.
I won’t even pretend to understand why that would have fixed it, nor why it would’ve been causing this problem to begin with. I’m just crossing my fingers that it really is cleared up for good.
* – (I feel the number of 'somehow’s in that paragraph adequately expresses my level of comprehension regarding the actual mechanics of whatever was happening here.)