Have you tried my thing?

https://github.com/Yonle/bostr

Try clear your relay list in your client and try to only connect to a bouncer. You could connect mine, which is public and there are peoples using it: wss://bostr.lecturify.net

List of relays that are being proxied / bounced is available at https://bostr.lecturify.net

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this is probably compatible with lol but incompatible with mom because mom looks at the IP when rate limiting.

You could still try to manually connect and set it as "write relay" in client if broadcasting in bostr does not work properly.