Internet service non-existent overnight, getting inconsistent replies from agents.

Since we moved into this house and set up service, my internet connection has been gone in the overnight hours. As in, it takes a few chores to get things up and running again each morning just to check some basic stuff. This seems like something someone with a little bit more knowledge than me might be able to troubleshoot, since there are patterns etc. 

I have called, emailed, tweeted... pretty much reached out in every way to Cox and they have told me something different every time that is both inconsistent and often untrue with data I have.

"I see you have packet loss, you have a splitter in your home don't you?" (said the Twitter person, when there is 0.0% packet loss and I only have one device connected in a tiny house)...

"The only way we can address your issue is if you pay for a technician to come out."

"I can't even find your modem." (yet random Twitter guy was able to test it from my non-wifi-data using cell phone tweet, again not associated with their service or affiliated with the acct, off my random social media to tell me about my packet loss?) 

To add insult to injury I am paying for a speed that was magically 10 mb more when I was "sold" it than what it is on my bill. The "tech support" person I spoke to this morning was not even tech support as they did not troubleshoot at all, they just tried to upsell me a faster service. They also told me I would not be able to stream anything at my current speed which I am able to do (they could not register in their brain "one computer/device" at one time as being something people use anymore?) 

This last call I kept being told about "faster speed" and it's not the speed... it's that when it does not work it DOES NOT WORK... and when it works it works fine, and this needs to be fixed. I would like it to be fixed to being reliable not just "hey got it working again, I will call you next time it screws up....so, talk to ya tomorrow morning!".... ugh. 

I saw a post here once about taking my complaint to the BBB et al, and that is the only way I can think of to solve this (or call attention to what may never be solved?) because I am being told to do literally nothing but spend more money to fix what I am already supposed to be getting with my monthly service charges/fees. When I call tech support they do not move me past Tier 1 with my issue, and I have had an account with them in some form for 15+ years (because someone mentions this every time I call... probably to rub it in/shame me for being stuck in an area with their monopoly...sigh)

 I really can't figure this out.