companies have speech rights that you would be infringing on by doing this
Edit: I know the issue becomes murkier for things like mom and pop shops and sole proprietorships, but I am willing to make distinctions based on scale.
If the corporation is being seen as a single entity then you should not consider it's employees' individual rights as the same thing. Or even combine them together to give more weight to the corporation's rights.
No it doesn't. The mom, the pop, and the sole proprietor are people; they have rights, which certain curtailments of their business might interfere with. The businesses themselves do not.