Membership management

I am thinking of re-building my existing Pensioners’ Association website using WordPress. It contains pages privileged to members who are required to log on for access. This involves checking details against a MYSQL database which is refreshed monthly from a stand-alone PC membership database. Only around 50% of the membership are online. I am looking ideally to integrate the membership database into a single master database which drives all membership maintenance functions as well as website access. It is managed centrally and members have no access to it. Also for example there is a monthly file extract for collecting direct debit subscriptions via BACS (UK payments system). Is this too ambitious for WordPress? I have looked at dozens of membership plugins and cannot see anything that meets my requirements. Can you suggest plugins to look at please? I am happy to answer further questions about my requirements.