To answer the OP's question, yes, CLP will remove copper fouling. Bring a lunch. Soak, scrub, repeat...repeat...repeat.
There are many specific copper removers. I prefer the M-Pro 7 series products as a compatible "family" of products, but there are lots o'options. Many copper removers are ammonia-based, which is viable but have some issues, mostly smell, toxicity, corrosion, and (some say) ammonia crystals after cleaning...which should be a non-issue if the bore is cleaned and lubricated after the remover is finished. The M-Pro 7 stuff is non-toxic and readily available. fWIW.