Emily,
It is always very hard to determine (based on short descriptions) whether or not someone's experience counts. Generally speaking, a project is a project, no matter what industry you are in. Therefore, if the work you did matches what PMI considers to be 'leading and directing a project' then you are good to go.
You say "I have never worked as a project manager". Do you mean to say that you were never truly in charge of the projects that you worked on, but instead you were a project contributor and someone else was 'leading and directing' the effort. If that is the case, then - unfortunately - your work does not qualify. But... if you are saying "I was leading and directing the efforts, but I did not have the official title of project manager", then you are good to go. It is the work you do and not the title you have that gives you the qualification.
1.) My number one recommendation is this: Look at the PMP exam content outline
www.project-management-prepcast.com/pmpoutline
and study the tasks in this document. If you can honestly say "yes, that is the work I did", then you are good to go.
2.) PMI deals with this often. A government PM who works on highly secret projects can still qualify. You have to give as much as you can then use "client confidential" or similar when needed.
3.) The contact person has to be someone in a position to confirm that what you wrote is correct. If the senior leader can do this, then use them.
4.) CAPM is an entry-level certification. It is a good 'fallback' if you determine that your work doesn't qualify. But I'd go for the PMP first.
...HOWEVER...
You also say "I don't necessarily intend to become a full-time project manager but I'd like to formalize this experience by getting my PMP certification". Are you aware that the PMP certification is only good for three years and then you will have to recertifiy? During these three years you have to earn 60 Professional Development Units that are VERY much focused on the work you do as a PM. And if you don't work as a PM then earning these PDUs is going to be really hard for you.
Until Next Time,
Cornelius Fichtner, PMP, CSM
President, OSP International LLC