My family couldn't live with the intermittent functionality. When the modem/gateway went into this state, VOIP was unusable (our only home phone) and internet game play was disastrously laggy. It was hard to troubleshoot as the family would reboot the modem instead of leaving it in a failed state so I could investigate.
I installed a moto SB6121 simple 3.0 cable-modem and an ASUS RT-AC66R router last night, in line with ChrisL's original reply. We'll see if this solution holds up. Thanks for all the help. The engineer in me wishes we could have driven to root cause.