I think a lot of results are "accessible" in terms of a pop science-y explanation, rather than following a detailed proof. And since you're looking for emotional motivation, I actually think the former is the more important!
For example, see this (quite engaging) video about moving sofas around corners.
Many of the mathologer and numberphile and such videos are very accessible, motivating, and quite well done (content and production and engaging presenters).
Heck, I would even include the Andrew Wiles doc by Horizon. It has some real connection to school age children (Wiles even says he was motivated at age 10). It doesn't matter so much that I don't understand the details of the proof itself. The problem is describable and a topical (literally naming "topics" in advanced math) explanation of the achievement is possible.
Probably a key thing is that the problem itself is describable (even if the details of the proof are not). For instance the Poincare Conjecture as a problem is tricky to understand, just as a concept. I mean I don't get it...so that must mean it's hard, right? ;)
You can maybe still mention that "they bagged a recent big problem" if someone solves the Riemann hypothesis tomorrow, but harder to really talk about the topic. And also note that it was the less general, but more understandable FLT problem that really motivated Wiles to his seven-year attic-sweat, not the more math-important (because of generality) Taniyama conjecture.
But I also would not underestimate the appeal of older "aha"s. After all, they are new to the student and are thrilling achievements of Man. I remember thinking Archimedes must have been a freaking time traveler when we learned his method for area under the curve of a parabola. Sure smells like integral calculus to me!
E.g. here is an engaging mathologer video on solving cubics:
Or this Veritasium video on Newton's advances in calculating pi (I might wait for a BC calc class, not do it in geometry though as the methods are sort of calculus and "algebra two").
So I wonder if the desire to highlight research results is more a desire of the teacher than the students. (After all the teacher is probably a math researcher or at least was one during grad school.) I did chem research during grad school, but was a bit skeptical (as a TA) of big wheel tenured profs at an R1 who wanted to connect in recent research results to a service course in undergrad chem (mostly non-major students, vast swath of pre-meds). Felt like they were trying to justify themselves and the whole concept of an R1 (which I do not agree is really beneficial for undergrad training). And they were falsely deprecating the importance to the student of learning concepts, tricks that are not new research results, but are new to the student.
P.s. But I would try to keep it light and motivational and not derail your course time with too much external content. Unless the kids are very strong to start with (thus tolerating more enrichment as the basic content itself is easier on them).
P.s.s. Also take a look at the American Scientist columns (or books) by Brian Hayes.
They are good popularizations. I dated an R1 prof who was doing cutting edge research in one of the topics (it was graphs or queuing or Hamming cubes or something like that) and she was impressed that I basically had an overview of her area from such a Hayes column. She took a look at the article in her area and said it was a lot better than she expected.