Earth is a closed system, so the shade cloth on Earth would simply warm up and reradiate the absorbed energy as infrared. Reflective mylar would see a portion of the reflected sunlight (which would have warmed the atmosphere upon entry) trapped by the greenhouse effect.

I don't know about that; land is expensive and inhabited by plants and animals, and you have to deal with wind. In space, there are other problems but at least you're probably not getting in anyone's way. You might also be able to use a much smaller shade, as it can be parked in L1 where it's always shading the Earth, and you don't have to deal with some of the reflected light diffusing through the atmosphere and not actually making it back out into space.

That said, I think the usual objection to the space mirror approach is that you can get the same result much cheaper by spreading a cloud of tiny reflective particles into the upper atmosphere. (I've heard of proposals that would just mandate some additive to the fuel used by large passenger aircraft.)

Making the sky 1% hazier is kind of uninspiring (especially when compared to giant orbital mirrors, which could also act as death-rays if aligned and focused properly), but if it's cheap and is likely to work, then maybe it's worth a try.

(Unfortunately none of these options is that they don't do anything about ocean acidification.)

Anything you build on earth is inside the atmosphere. Keeping heat away from greenhouse gasses is the whole point.

Objects in space are generally also subject to less weather, and as such they don't materially degrade. You could make a shield out of opaque film that would tear to shreds at the slightest breeze (see JWST sun shield)

The easiest surfaces to make more reflecting should be the oceans. Some proposed carbon capture methods involve algae. Maybe algae could be synthesized that are white/reflective as well as capture carbon? Patches of algae can be huge without the need for any construction.

That's why you set up orbital infrastructure so that you don't have to bring up everything from Earth and can just mine stuff in space.