Neat stuff - certainly this problem crops up quite a lot where an internal server needs to get GitHub webhook data.
In the past, I've had good luck using a webhook proxy. I've mostly just used https://smee.io/ which is simple and lightweight although seems to be mostly abandonware at this point. I dockerized it so that it could be used in a Kubernetes cluster, which was very useful for my GitHub Actions build cluster: https://github.com/ethomson/smee-client
There's also Hookdeck, which I haven't used in production, but have played around with, and it seems conceptually the same, but can be made more Enterprisey. Whether that's a bug or a feature is probably up to you.
In the past, I've had good luck using a webhook proxy. I've mostly just used https://smee.io/ which is simple and lightweight although seems to be mostly abandonware at this point. I dockerized it so that it could be used in a Kubernetes cluster, which was very useful for my GitHub Actions build cluster: https://github.com/ethomson/smee-client
There's also Hookdeck, which I haven't used in production, but have played around with, and it seems conceptually the same, but can be made more Enterprisey. Whether that's a bug or a feature is probably up to you.