That anti-seize is a mix of aluminum, copper, and graphite. There is also just copper and graphite anti-seizes available that is rated at 1800°F, and then there is the nickel and graphite one I mentioned are rated at 2100°F. How often one actually gets to higher temperatures for long enough to matter, I can't say. If you assume 4500°F to 5000°F powder combustion temperature at peak pressure and that it drops to around a third to a half of peak pressure at the gas port, it might still be in the 2000°F range, albeit briefly.
For carbon, if Slip2000 Carbon Killer seems too harsh, Gunzilla will penetrate and soften carbon, albeit more slowly. I once had it remove all the hard carbon and rust from a pitted bore, causing both to just fall out of the pits and leave them bright steel-colored. But it was sitting for about six weeks. I've also had it soften carbon rings at the end of a chamber in about 24 hours. None of the other penetrating oils or other gun cleaners have done that for me.
Another recommendation I've seen is a long soak in Mobil One motor oil, which has carbon cleaning agents in it, too. But I find it works better on new, warm carbon than on cooled and hardened stuff. But if you have some or if you want to try it in place of the anti-seize, it might keep carbon down if it isn't blown out of position.