I think Chambers would consider this an easy problem, assuming the mind did not have to have phenomenal experience to qualify.
A lot does ride on what is meant by “engineering”. Do GANs qualify as a type of engineering? The adversary could be viewed as selecting for fitness.
If by mind we mean human adult mind, then we could engineer only a baby’s mind (or perhaps even a fetal precursor) and then rely on encultured action to develop an adult human mind. Possibly that action could take place in a virtual world. Far from current technology, of course, but still easy problems in the Chalmers classification.
I do agree with the linked paper’s conclusion that there are domains of knowledge, like morality, that cannot be addressed solely by science.