Geoffrey,
It sounds like you do have some business analysis experience even though most of your recent work has been more data focused with the integration of off-the-shelf systems. Your current project will probably expose you to some Finance experience which is where you seem to want to work. Next, I would look for a project (may mean switching companies) where you are working in the Finance domain but doing Business Analysis/Systems Analysis for a custom built application. As you are doing so, be sure to constantly improve your skills and Business Analysis competencies by taking training courses or through self study online.
Anytime you go in for a BA interview, be sure that you can not only state "this is the experience I have" but also "this is want I have been doing on my own to improve my skillset".
While we are on the topic, many seem to think that once they reach Senior BA that the next step is Project Manager. I find this to be completely inaccurate. All BAs should have some project management skills, but Project Management is more of a lateral move. Consider moving into an Analysis Manager role where you are managing a team of analysts on a larger project. After that you can either stay on the BA side developing a Business Analysis Center of Excellence for your organization, or move into Program Management (i.e., running all aspects of a project including analysis, development, testing, etc.). For Program Management, some companies may require you to have at least some background managing development teams and QA teams, while others may not. A good manager can understand enough to manage the experts in these areas and let their team drive the details that they themselves don't fully understand.