Huge bummer. Prevents almost everyone from using this and recouping their costs.
I suppose motivated teams could reproduce the paper in a clean room, but that might also be subject to patents.
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.
We should also have a fund for particularly tricky inventions and copyrights that would greatly benefit mankind.
Say, someone or some institution writes a good school book. We can just buy the book for whatever we think is reasonable. If they want to publish the same book the next year with the chapters shuffled around they could be entitled to a tiny fraction of the previous sum or it could be denied for being spam. If this bankrupts the company is of very little interest.
(tangentially, like another comment briefly mentioned, are models actually copyrightable? Programs are, because they are human authored creative works.)