I think that the second part of the proposed amendment (money is not free speech) goes in the right direction.
The first part ("Artificial entities established by the laws of any State, the United States, or any foreign state shall have no rights under this Constitution") would be disastrous. Do you want your ISP to have no rights against unreasonable search and seizure? You could fix that a bit by another amendment getting rid of the idea that individuals lose their 4th amendment rights when their information goes to a third party, but I'd still prefer that the government not have free reign to search corporate offices.
Keep in mind too that advocacy organizations are usually corporations. Would it be a good idea to say that the ACLU or the EFF has no due process rights, so that a government can, say, dissolve it on a whim?
Most of what people want could be done statutorily. The Hobby Lobby decision was a statutory interpretation case. The result would have been completely different if the Religious Freedom Restoration Act had a clause saying that its provisions only applied to "natural persons."