What are some methods to limit beta roll-out where the app will rely on viral sharing via social media for it's ultimate success?

If your product relies heavily on a successful growth-loop through social sharing, you simply *must* run the social component "live in the stream." The value of the data you will collect far outweighs any concerns over someone guessing what you're doing by the social shares.

See my answer about what makes a great technology product here on Clarity about the importance of a great growth loop.

The ultimate thing you'll be able to learn via the public test is the effective of your messaging and a general click through rate. You can bring them to a page that playfully says that the link was generated by an app in private-beta and if they want to learn more, they can sign-up. That in fact, would be another great data point.

The point is that just by making your social stream messaging and link public doesn't make your product in any way public.

And by the way, the more effective your social share is at generating click-throughs or full-blown conversions (a click on the landing page of any kind), then the higher and stronger signal you have to the fact that you're on to something.

In a call, I'd be happy to share my experiences in building MVP's with contract labor and testing growth loops via social streams.

Do you know how Mailbox App did it?

They had a closed beta but they hard a website, a landing page and an iOS Application that enabled people to register in queue waiting for a slot be to accepted into the closed beta.

People had a newsletter delivered to them and were able to share and invite others (this social actions pulled them ahead on the queue). This way people could interact, share and receive newsletters on Mailbox App even though they were not included on the closed beta. It was a successful strategy and other companies did it also with success.

Read this article to know more about it and how you may be able to do it also:
http://techcrunch.com/2013/04/01/queueing-theory-lets-any-app-offer-a-mailbox-like-reservation-system-even-if-its-just-for-building-buzz/