The hazing and spider-like cracks can be taken out, but it requires a lot of material to be taken off. I've done this several times with aggressive sandpaper, 240-320, and a random orbital sander. Then you work your way up to about 1000 at least, I go up to 1500-2000. Then polishing compounds and wax.
If you're interested, you can send me your headlights and I can repair them for you. If can use another car, or have an old set you want to send. Let me know if you're interested and we'll work out a price. I guarantee them to look like new when I'm done. Except for any major cracks or chips of course.
If you tackle this yourself, get high quality sandpaper, and be patient!
Later,
Lee