Funny you mention this as I just tried it for the first time this weekend just by accident and like the results, cleaned the carbon off and easier on the finish than the brass brush. I think it's going to be a winner!
CLR works well on carbon. If neutralised by flushing with water then light oil, no problems. I stupidly left a a droplet on top of barrel for a few minutes. It blemished the parkerized finish. I now only apply it with a Q Tip swab where I want it and clean any drops with H2O. Quickest brake cleanup after heavy use (223 1.200 rounds). is diluted simple green in ultrasonic followed by CLR and brass brush /brass scraper. 10 minutes from caked to pristine.
Peroxide and vinegar works great for dissolving lead, but it also makes Aqueous lead acetate in the process. It’s a nasty chemical that can give you lead poisoning so take precautions and dispose of the byproducts responsibly. It’s commonly referred to as “the dip” in the suppressor community due to the effectiveness of removing lead.