I saw a client with this issue. We removed the router and connected directly to the ISP supplied modem and it still dropped. The ISP said that was normal. So if your ISP is winking out once in a while and keeping in mind that recent weather event, you have choices to make.

About the DMZ. I think they mislead you. When I use the DMZ I never use the word "hosting." If we drop that word we only need to put the IP address of the machine we want to be in the DMZ in the router DMZ settings. I will not go any deeper than this because folk must be comfortable with that change. If not, they should not be in that setup page.
Bob