Okay, a few points:

1. In addition to using Yoast to noindex archive subpages, you may want to also consider seting it to noindex both tag and category pages.

These are found in Yoast under "Titles and Meta > Taxonomies"

2. While the Yoast plugin will put a "Noindex" tag on the page, this doesn't remove it from Google's index right away. Google first has to crawl the page. Using the index removal tool does help.

3. If your site dropped from 320 visits a day to 30, you may have different problems than duplicate title tags and/or content. Not sure what to tell you to look at, but backlinks, penalties or something else may be to blame.

If you're interrested, here's a great (free) webinar on Wordpress SEO http://moz.com/webinars/advanced-wordpress-seo

Here's my take:

First, basing user experience on cookies isn't always the best experience. Folks change browsers throughout the day (phone, tablet, laptop, desktop) and they often browse privately and/or clear their cookies. This means LOTS of folks will be landing on the "first-time" page when they are actually returning visitors.

But if you can live with this, fine.

From an SEO point of view, where are you directing bots like Googlebot that don't accept cookies? Will bots see the "new visitor" page? Do you want bots to see the new visitor page?  (sorry for so many questions, but I don't know your objectives - but these are important questions to think about)

Overall, it's typically best to have a consistent experience between bots and visitors. If this means javascript popup for folks without a cookie set, this might be the best option (but still not ideal, because popups can negatively effect visitor usage and satisfaction metrics, like bounce rate)

If this is something you have to do, I'd go with the popup, but first I'd try to talk the client out of it