Set EOT based on time of year

We have a non-profit organization that people buy memberships to, and until recently we were not able to hook up our bank account to paypal, so we’ve been managing payment offline, then updating EOT manually. Now that the we have paypal set up, we want to start accepting membership payments online. My question is primarily how to set up Automatic EOT so that:

1) Users that subscribe before Oct 15, get their EOT set to Jan 31 of the following year (i.e. if they sign up Oct 14, then approx. 3.5 months later).

2) Users that sign up after Oct 15, get their EOT set to Jan 31 of the next year (i.e. if they sign up Oct 15, then approx. 15.5 months later).

and although unlikely, is there a way to insure that if a user signed up let’s say Oct 15, and then sees the membership drive in January, and forgets and signs up again, that they’ll get told they’re already signed up for the following year and not to pay again?

Thank you.