Issue appears to be solved.

Had a fairly long multiplayer session last night and no one got disconnected.

I believe 10.156.0.1 is the cable modem gateway. The new modem has more info available. I can see its external IP and it is in same subnet.

While playing I still rarely see ping packets get ...

I was able to capture some data with pingplotter and found that hop 1, my router responded fine, but hop 2, [10.156.0.1] would not respond during the issue.
I think that hop would be my cable modem?
Maybe it is as you said, it is getting overwhelmed with # of packets and locking up.
I was able to ...

Gracias Caennanu for the suggestions.

Discord will notice there is a problem and disconnect after about 30-60 seconds and start trying to reconnect, but I hear everyone talking about having lost connection to server until then.
Factorio has started showing messages about them being disconnected ...

EDIT: Solution was to get new cable modem.

When my friends and I are playing on my headless server my outbound internet will (randomly?) once every 2 - 4 hours of continuous play stop working requiring me to reboot the cable modem.
We are just doing random stuff, we haven't noticed any pattern ...