Hi,
From what you have described and what interests you, I think becoming a BA may make sense. Your best bet might be to leverage the existing experience you have within the investment bank (hopefully you have some good industry knowledge) and start to volunteer for smaller BA type of roles. However, before starting be sure you take the time to read up on business anlaysis methodologies, processes, and skills required. You don't have to be the expert on all of this starting out, but you should have an awareness of some of the methods and processes used to perform in a BA role and know where to find answers if you are confused or need information. You came to ModernAnalyst.com so you already have one very important resource at your disposal.
On another note, you mentioned maybe becoming a PM. I'm curious, how would you describe the role of a PM versus the role of a BA?