Essentially, most of the active clans on your server will have opened academies. All you have to do is find out about a clan you like and approach them.
Clans absolutely love academy characters. Virtually every level 5 and above clan is in a major push to get reputation points to level the clan, and academy characters are the best way. What nameless meant is if you don't think the clan is doing enough to help you, you have a million other choices.
If there was a way to set it so that you can hide main clan stats, chat, and ally chat from Academy members then I would allow outsiders into my academy. Othewise.... alts it will have to be.
Considering the war status of most clans hitting lvl 6 and the fact that the academy has full access to clan and ally chat and most likely the ally vent also.. Its a huge security risk to invite random lowbies.