You'll also want to look at membership software, since I believe that is the functions you need.
I have some familiarity with Catholic Daughters (my mother has been a member for 60 years) and with Fund EZ and I'm thinking that Fund EZ may be a little bit of a stretch to support your needs. I'm also concerned that since you are running such an old version you may not have any support. If that database crashes, do you have a way to recover the data from it?
You aren't too far from the Knights of Columbus headquarters; I'd ask them what they use. Other membership orgranizations with dues billings, etc., might be good to check with as well. People who do the same kind of work you do would be the best sources of new information.
As someone who writes custom databases, I believe that is often the best way to go, but I can't recommend that to someone who doesn't have in-house staff to provide support. But you may find another organiztion that has a custom package that you could use as well.