There's currently little recourse or penalty for abusing the DMCA. What should be done is make companies liable to the user affected for issuing a willfully abusive request. If companies faced the same $150000 penalty willfully making a false DMCA request as exists for copyright infringement they would think twice about doing this.
DMCA abusers should have their copyright for the work in question nullified; it should go straight into the public domain. Companies that ignore fair use no longer have any moral right to that work.
How would that work for companies placing DMCA requests for works that they do not own? (I agree with the sentiment, and the poetic justice of the idea, but am curious on the edge cases.)
IIRC you already swear under penalty of perjury as part of filing a DMCA request, so presumably you could sue for money and include this fact as part of your argument for punitive damages (IANAL).
Imprison the executives, for a crime tantamount to theft. (Though umprisonment for fraudulent DMCA takedowns regardless of whether or not they own the copyright would be justice.)