OK -- since no one else is replying -- I thought I'd go ahead and post what we decided to do. Maybe someone else has a better way, but this is what we did.
I created a contact form called "Outgoing Contact". Within the form are items like "Pastoral Call (Josh)" and "Pastoral Call (Bill)". With the name in parentheses indicating to whom that item is assigned. When we make outgoing contacts, we go into the individual view of the person we're calling and click the " + " sign next to the contacts area. We add the contact there and then (usually) immediately close the contact.
What would be really helpful is if we could open and then close the contact all in one step -- like with a "close" checkbox right there on the same screen where you can enter notes about the contact. Maybe I should post this in the ideas area.
Is anybody else doing anything like this?