Is there anything I can do to achieve just one Initial Connection, instead of several?
http://www.webpagetest.org/result/110920_7N_b71915aea8e1ea526a76a4f254569881/
Not without inlining everything into the base page and reducing the whole page to a single request. The additional connections actually help, otherwise each request would have to wait for the previous one to complete and the images would not be able to load in parallel.
Thanks for the explanation, Pat. So the “extra” connections are there to accommodate parallel downloads, and not because there’s something wrong with my setup! I suspected that might have been the case, but I wasn’t certain. 
Yep. IE7 would do up to 2 parallel connections per domain. IE8 and the rest of them do at least 6 per domain (as needed).
super