One more structural option worth considering before the mitigations: change what you expose.
Right now your proxy is essentially a free version of the paid service. Anyone who finds it gets exactly what you pay for. That is the strongest possible incentive to abuse it.
If you can narrow the proxy — restrict which queries it will forward, transform the response so it is only useful in your context, limit parameters to a fixed set — then the endpoint stops being a general-purpose free tier for someone else's product. An attacker copying it gets something much less valuable, and the incentive largely evaporates.
That is usually more effective than any amount of request signing, because it attacks the motive rather than the mechanism.