Multiple passwords for a user?

I’m running a website for our church that has a members-only area; using the plugins “Page Restrict” and “WordPress Access Control” to ensure security.

For our church of about 300 people, it would be crazy to assign everyone usernames and passwords; so we’re just using the login name “Church member” with password “easily remembered password” and distributing it to all 300 members. [Names changed to protect the innnocent]

If I want to change the password occasionally (maybe twice a year?); is it at all possible to have a “grace period” where the old and new passwords will both work – and the people using the old password are told that they’re using the old password, which won’t work after (insert date)?

Thanks for your help!
Chris