A strategic countervalue exchange does have a chance of reducing solar input for a while, but the effect would be comparable to taking a man dying of a fever and dumping him in a bathtub full of ice. The winter kills off a ton of photosynthesis, and then the hotter temperatures have less fighting them, there's even more carbon in the system. It's much worse.
End game would be the same, but accelerated: the collapse of human systems across the board, which is where big lethality numbers come from. The faster that collapse, the deadlier it is, the more human systems go down for the count. Humans survive in a changed world, but they've largely deindustrialized, and very possibly revert all the way to hunter-gather-scavenge.
Hydrocarbon reduction, it's needed of course, but we're way past that. We've known for a literal century, after all. Today the only way out without systemic collapse is to adopt big industrial cooling methods. Basically doing nuclear winter, but in a controlled fashion to smooth out the warming to its new optimum, combined with hydrocarbon throttling. The "Space Parasol" is my favorite of these methods, as it's easy to turn off, unlike the "Let's Add Lots of Exotic Dust to the Upper Atmosphere That Might Or Might Not Come Down". Or any of the many bio-engineering solutions that, uh, have ample room for "nightmare", like the idea of covering the planet in Super Bamboo[1] - causing possibly the worst ecosystem crash since the Cambrian. There's such a thing as too much oxygen, you know . .
Rich guys should be clocking each over the head for the chance to build the Space Parasol, because if you make the place liveable, you can charge the entire planet rent. "Oh, you don't think it's worth it? Weeellllll . . . ."
Long term, it's not like the planet's especially hot right now, geologically speaking - Paleocene-Eocene Thermal Maximum (PETM) Antarctica didn't get colder than 16{deg}C - it's just all the liberated volatiles from the frickin' Carboniferous making it hotter faster than Holocene natural systems can compensate. Whether our technological systems do any better than natural systems, heh heh heh, that'll be the question, won't it?
[1] If I am being honest, if we do pull through all this crap, the bioengineered future seems the most likely one. I have a very diminished faith in humanity pulling off megaprojects like a Space Parasol.