Not sure if anyone else will find this useful, but I wrote a very quick and dirty fallback skill that sends your utterance to Kagi’s FastGPT service and reads back the response (minus the references).
Works with a Kagi API key, which uses API credits, or with your session link if you’re a subscriber, which doesn’t need API credits but is a little more dicey (it’s making requests the same way their web UI does, which isn’t really a documented API meant for public consumption).