I would've just sent the DMCA notice. It's not a "whole process", it's a couple lines of text you copy/paste, put in the URL of your site and the copy, change the date, and email to the host. It'll take you a few seconds to modify and send out. Most web hosts have a specific mailbox for DMCA notices on their contact page or in their AUP.
Subject: DMCA Notice of Copyright Infringement
The copyrighted work at issue is the text that appears on: [URL(s)]
The URLs where our copyrighted material is located include: [URL(s)]
You can reach me at [email] for further information or clarification. My phone number is [phone] and my mailing address is [physical address].
I have a good faith belief that use of the copyrighted materials described above as allegedly infringing is not authorized by the copyright owner, its agent, or the law.
I swear, under penalty of perjury, that the information in the notification is accurate and that I am the copyright owner or am authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.
[your name]
[today's date]
Never once have I had a DMCA notice not result in the material taken down within 24 hours, even when the host was outside the US.
None of them want to potentially be a party to a copyright infringement suit, however unlikely it may be that you'd take it to court and drag the host into it.