Thanks for your inquiry. ~ We appreciate your patience :-)
Yes I believe we can help you w/ s2Member® Pro.
1. Free registrations only
2. Multiple free account types (Pension, Business, Advisor)
Yes, this is possible with s2Member® Pro Forms.
See: Knowledge Base » s2Member® Pro Forms
See: Video » s2Member (Free Registration On Multiple Levels?)
3. No cross-category content (Pension accounts only see Pension content, Business accounts only see Business content)
Yes, please use s2Member’s Custom Capabilities for this. You would provide Free Registration Forms, using Shortcodes like these, where you provide access to specific Membership Levels, and to specific Custom Capabilities. Note that Custom Capabilities provide access that is not incremental like Membership Levels are. So using Custom Capabilities together with Membership Levels is quite powerful.
[s2Member-Pro-PayPal-Form level="1" ccaps="pension" .... /]
[s2Member-Pro-PayPal-Form level="2" ccaps="business" .... /]
[s2Member-Pro-PayPal-Form level="3" ccaps="advisor" .... /]
See also: Dashboard -› s2Member® -› API / Scripting -› Custom Capabilities
See also: Video » s2Member (Custom Capabilities)

4. Individual registration forms for each account type (no drop down, radio button, checkbox, etc. for selecting account type)
Yes, please setup Registration/Profile Fields with s2Member, and narrow down some of these custom fields to specific Membership Levels. This way when you display the Registration Pro Form that provides access to Membership Level #1 with Custom Capability “pension”, s2Member® will be displaying all of the Registration/Profile Fields configured for Membership Level #1. Do the same for Membership Levels #2 and #3.
See: Dashboard -› s2Member® -› General Options -› Registration/Profile Fields

5. The registration forms have to co-exist on the same page (one page will have the Pension and Business form on the same page)
Not possible with s2Member. We allow only one Pro Form on each page. So if you generate three Pro Forms (one for each Membership Level and Custom Capability), they need to be introduced through Pro Form Shortcodes that are inserted into a Post or Page of their own. You could have a one page that contains links/promotions for two different types of accounts, but the actual registration form needs to be on its own Post or Page.
6. Export members/users/registrations to CSV
Yes, this is possible with s2Member® Pro.
7. [Nice-to-have but not strictly necessary.] Double-opt-in (Visitor signs up on website, gets email with link to click through to confirm)
Yes, you can integrate with either AWeber, or with MailChimp (or both if you like).
Please let us know if you have any other questions/concerns :-)