I agree. You'll be notified in GWT. Forget about trying to get you site in DMOZ. Submit it and forget about it. I have been trying to get into DMOZ for a couple years now.

BUILD quality content on your landing page. Watch this WBF: http://www.seomoz.org/blog/the-new-onpage-optimization-whiteboard-friday

What I would probably do is build the whole thing out on the test.example.com and move the website from there to example.com.

Would that screw up SEO if we forwarded that domain to www.mydomain.com/social or social.mydomain.com and built links to that?

If it's a new subdomain without link juice, just transfer the files to a folder.

I don't know if this will help out at all, but I'm putting it in here to demonstrate different softwares.

1) http://www.shipoverseas.com/ MAGENTO

2) http://www.shipoverseas.com/blog/ WORDPRESS

These are two completely different softwares, but the menus are the same. As you stated, you have different menus. WHY? What softwares are you using and why not just "bridge" them with a plugin?

1) Do you think it would be professional to have the social site there with a different look?

NO. I think more people would stop and wonder if they are on the same website.

I am looking forward to your response and would like to help

Buy this book. It covers what you are looking for. This book was written by Danny Dover, the former Lead SEO for SEOMOZ.

http://www.amazon.com/Danny-Dover/e/B002IR161U/ref=sr_ntt_srch_lnk_1?qid=1332304804&sr=8-1