this is probably compatible with lol but incompatible with mom because mom looks at the IP when rate limiting.
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
Discussion
You could still try to manually connect and set it as "write relay" in client if broadcasting in bostr does not work properly.