Assuming you don't mind committing perjury, I guess.

Is there actually a recorded instance of someone getting charged for perjury relating to a DMCA request?

I don't know what happened with this case: https://torrentfreak.com/warner-bros-our-false-dmca-takedown...

The law is pretty clearly broken. I kind of hope Google is collecting all the false take down requests they get.

Submitting a false report, under penalty of perjury, and saying "whoops algorithms lol" shouldn't be something they get away with.

There's this too: https://www.eff.org/press/archives/2004/10/15

Only one part of a DMCA takedown is under penalty of perjury, and it's quite possible to file a knowingly false takedown request without that part being falsified.

But isn't it the part where you assert in good faith you own the copyright? How do you get around that scenario of a malicious takedown request against a random site?

It's the part where you asset that you are the owner of the copyright you alleged is being violated. As long as you own copyright on something that's not a problem. The part where you actually allege that particular content uses your work without permission or privilege is not under penalty of perjury.

Yes because hackers who go around DDOSing entities care about perjury

To be fair they were talking about pentesters, for whom port scanning is usually on the table, and breaking the law is not.

Under Computer Fraud and Abuse Act (18 U.S.C. 1030) it is a federal crime to "intentionally access a computer without authorization or exceed authorized access" ...

An eager prosecutor could take that and run a mile