Trying to attach a license to model weights seems counter-productive to me. If you argue they are copyrightable then surely they are derivative works of the training data, which is unlikely to all be public domain. Machine learning enthusiasts are better off lobbying for model weights being non-copyrightable as it doesn't have any creative input and is the result of a purely mechanical process.

The copyright on the code, on the other hand, would definitely be copyrighted and would need a clean-room implementation, as you said. The community could pool its resources and do it once, and license it under the AGPL to keep it and further improvements available to everyone.