Perhaps you'd be so kind as to review and critique the timeline below
Here goes...
Assume ...
If I assume you have everything set up correctly then I'm not going to get very far in helping you solve your issue.
Wonder why.
Stare at WP-MU Admin panels for 15 minutes.
Google ~20 variations of "How to configure WordPress MU Domain Mapping"
In despair, DRAFT this post
I appreciate your frustration. However adding commentary like this makes it more difficult to read the information you have provided.
On with some troubleshooting assistance...
The 'Too many redirects' message is an indicator that there are one or more rewrite rules in your htaccess that are rewriting a URL to itself.
When you created the new site did you check to see if the front end of the site loaded before you added the domain map? If so, how long did loading the front end take? If it does not load within a second or two then there is something wrong with your webserver configuration (possibly the rewrite issue). If that's the case, contact your support for your EC2 instance.
PRIMARY - visit http://rennickmedia.org, http://rennickmedia.net & http://rennickmedia.com in separate tabs. All 3 sites are domain mapped to the same site. The .com domain is the primary domain.