When people hear “free trade” they think of a system that waives all import duties, which may or may not be what is desired here. I can think of some bad actors passing a “carbon tax” just to get all the other duties on their goods dropped.
Honestly, this is exactly what I was thinking when I formulated this question. While I agree with your comprehensive list, we may not have time for that. Even a 10 or 20 year deal of a “carbon tax free trade agreement” may be all we need to course correct. If it is effective (at curbing carbon emission and as a political tool) a new FTA with the qualifications you listed could be crafted. The more qualifications, the slower nations would be to adapt/enroll and I’d be wary of adding too many if the goal is fast action now.
Bad actors’ intent matters little, as long as their actions align with world goals.