I would do this, but have it redirect to the original site. You could even add canonical tags in the head section so that Google sees it as a duplicate copy of

I would do this, but have it redirect to the original site. You could even add canonical tags in the head section so that Google sees it as a duplicate copy of the original site and doesn't index it. This basically makes their site not exist. Then you can work on the DMCA takedown in parallel.