Client owes $30k in freelance web development fees, has ignored demand letter - is DMCA takedown a good option?

In late 2015 I helped a company totally revamp their B2C sales website - some highlights include making it mobile responsive and switching payment processors from Authorize.net to Stripe.

However, they haven't paid for 3 months worth of work at the tune of $30k USD; they were acquired and claimed there were accounting issues that needed to be figured out before they could render payment, but after a year of that same excuse I figured I was getting played.

There is no contract unfortunately but there are in-depth email chains (including multiple emails acknowledging the debt and my having done a great job) and detailed invoices, along with a Github repository with my commits as well as line item sheets proving the work was done. There are also previous paid invoices from both the company and their acquirer. There are NO concerns of non-performance on my part - I delivered all that they asked, this is literally just them refusing to pay.

I hired a lawyer in November 2016 to send a demand letter to both the client company and their acquirer which was sent in early December 2016 but it's been a month and I haven't heard back from either entities.

The lawyer is suggesting a DMCA takedown (for additional money of course) but won't explain the pros / cons / ramifications of such a move and I'd like to know more about both the probability of success and the potential legal repercussions.

So basically, three questions:

1. Is a DMCA takedown of the website a good idea, assuming my goal is to get paid? Why or why not?
2. What are alternative options for me to get paid, and their associated approximate cost / effort?
3. Everyone seems to be against calling out the company / founder by name but again I don't quite understand why. The founder is fairly well known in the Bay Area and I have a feeling that public shaming would actually be enough of a catalyst to get him to pay. Would love to better understand the ramifications of this decision as well.

Happy to answer further questions, thanks so much in advance!

I'm currently in Austin, TX but did the work in Jacksonville, FL; the client is based in NJ and the acquiring company is based in CA. It's complicated... :(