This guide runs CLIProxyAPI in an Amp orb around the clock and publishes it at a stable public HTTPS URL through Tailscale Funnel. An Amp Custom URL model-routing connection then sends Claude requests there, and CLIProxyAPI serves them with your Claude Pro or Max subscription (OAuth login) instead of Amp credits.
The host scripts, templates, and an agent skill that walks you through every step live in ben-vargas/amp-plugins/skills/amp-cli-proxy-api. The easiest path is to install the skill and ask Amp to set it up:
amp skill add --global ben-vargas/amp-plugins/skills/amp-cli-proxy-api