Hey Richard,
First, note that the estimated number of pages displayed by that is an estimate which gets refined the deeper you go into the search results. On page one, they tend to be wildly inaccurate.
If you go all the way to the end (page 13) and then repeat the process with ommitted results included you still get to page 13, and a total of 123 pages. (Somewhat better than the 2k+ results.)
This is less than the 716 pages you mention so maybe you've got he opposite problem? What do you see if you check your google analytics and webmaster tools? Which pages are getting organic traffic from google? Which pages are showing in the search results (Webmaster Tools, Impressions)
What are the pages you want to appear in search and what are the keywords you're targeting?
My first thought is - if you're allowing people to design your own jewellery - are you also allowing them to easily share their creations on social, etc? Have you got embed codes so that they can put their designs on their blog etc? If you're not then I think you're missing a trick.
All of these individual items, designed by users, will (should) all be linking back to the specific category pages (or other landning page) and increasing the authority of that page. Make sure your category/landing pages have good unique content that communicates both the value proposition and the products you've got available.
If you don't have these category pages, then it might be worth looking at your site architecture/hierarchy and think about creating them.
Your individual product pages might get long-tail traffic (and having lots of different variations, described in real-people's own words might actually work to your advantage here), your category pages should be the ones targeting head terms.
I notice you've no-indexed and no-followed the product pages in question. This means that if these pages are shared, then any inbound authority/link equity/link-juice/ is just being discarded. Are you sure you want to do that?
I don't think you need to worry too much about google's index at this point and I certainly wouldn't consider deindexing the whole site.