Hi,
for what its worth my advice is
1. thoroughly internalise what being a BA is all about and it looks to me as if you have made a superb start on that - anyone who can read the BABOK and BPMN manuals and remain interested is worthy of respect! :-). Training courses would also help (however, be aware that as a training provider I would say that wouldn't I???). I do have a reading list of more accessible books than the BABOK if you would find that useful - but there are loads of good ones out there...
2. get a role (contract or perm) on a change project in any capacity at all (almost - you just need access to project progress meetings)
3. without telling anyone, promote yourself in to the role of BA by volunteering to assist in BA activities, especially ones in difficulty - and now the hard part where you make or break it as a BA (in that organisation anayway): add value by clarifying the analytical issues and then solving them with appropriate user and other stakeholder engagement
4. if you are successful in step 3 you will natrually migrate to the role because people will seek you out as your reputation for solving BA problems grows. Pick your moment to try and formalise your job title as BA and/or apply for other BA jobs having written your cv to emphasise your experience is performing the BA role if not actually being called one
I'm pretty sure this method works as quite a few people I know have done it - including me!