CARP not preempting despite "disable preempt" not checked

[MaeveFirstborn]

We have two firewalls in a CARP failover relationship. Each one has two WANs and three LANs. While troubleshooting something earlier today, we realized that CARP failover wasn't behaving how we thought it was supposed to. We want the behavior to be such that if one of the interfaces fails - any of them - the backup takes over. More specifically, whichever one has the most functional interfaces. I guess a better configuration in the future would be to aim for specifically weighing on the WANs, but for now we want to get preempting working in the first place. 
Right now, when we kill one of the interfaces on the master, the second firewall's corresponding interface takes over as CARP master. However, ONLY that interface takes over. Which is useless - if the WANs fail on firewall 1 but the LANs don't, then the downstream hosts are going to send messages to the firewall which has the CARP master - which in this case is the firewall without WAN reachibility. 
Is it something with these advskews?
Obvious stuff:

• Disable pre-empt is off
• CARP itself is working, just not in a group