About to give up! SBG6580 service issues

I have called support so many times in the last year that I've put them in my speed dial.  I have a Motorola SBG6580 which I've replaced twice now after support and on-site technicians have told me that it "could" be a hardware problem.  I've had 5 different techs come to my home, including 2 contractors would were completely worthless.  They all have said the same thing - dancing around the issue of internet speed issues and intermittent packet loss.  I work in IT and support an international business which requires me to work late hours and some overnights to support our Asia offices. Here's my issue:

Every night around 1:00am CDT, my speeds drop like a rock and sometimes stop entirely.  When I call, support can't see anything wrong with my signals.  They have me reboot, etc like the script says and it never resolves the issue.  Service call scheduled.  Service techs arrive during the day when I don't typically have said problems, can't find issues, close service ticket.  Repeat.  Repeat again.  STILL having problems.  Last time I called, the support people scheduled a tech to come check the line into my home.  The first tech came out and told me that the 'ends' on my cable from the alley to my junction were bad, so he replaced the one into my box but NOT the one on the pole.  (He admitted that he didn't think it was the problem, and he didn't want to climb back up there again...)  Did not resolve the issue.  Second call to support scheduled a tech who replaced the entire section to my house from the alley.  He stated that if that didn't fix the problem, that I should call and schedule a rewire of my home since we have the whole-home coverage plan that would rewire at no cost.  I called and scheduled a rewire.  They sent a contractor who stated that there was nothing he could do since they weren't allowed to go into my attic and I needed to reschedule. 

Today, when I am finally having problems during the day, support still can't see anything wrong on their end.  I log into the router and find that my log is full of service errors and warnings.  The warnings include:

DHCP RENEW WARNING - Field invalid in response v4 option;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=a4:4c:11:8b:3d:8b;CM-QOS=1.1;CM-VER=3.0;

 TLV-11 - unrecognized OID;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=a4:4c:11:8b:3d:8b;CM-QOS=1.1;CM-VER=3.0;

DHCP WARNING - Non-critical field invalid in response ;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=a4:4c:11:8b:3d:8b;CM-QOS=1.0;CM-VER=3.0;

No Ranging Response received - T3 time-out 

Received Response to Broadcast Maintenance Request, But no Unicast Maintenance opportunities received - T4 time out;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=a4:4c:11:8b:3d:8b;CM-QOS=1.1;CM-VER=3.0;

No Maintenance Broadcasts for Ranging opportunities received - T2 time-out;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=a4:4c:11:8b:3d:8b;CM-QOS=1.1;CM-VER=3.0;

DHCP FAILED - Request sent, No response;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=a4:4c:11:8b:3d:8b;CM-QOS=1.0;CM-VER=3.0;

SYNC Timing Synchronization failure - Failed to acquire QAM/QPSK symbol timing;;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=00:00:00:00:00:00;CM-QOS=1.0;CM-VER=3.0;

and

SYNC Timing Synchronization failure - Failed to acquire FEC framing;CM-MAC=e4:83:99:71:25:cc;CMTS-MAC=00:00:00:00:00:00;CM-QOS=1.0;CM-VER=3.0;

to name a few that are the most reoccuring.

I'm fed up with getting the run around and not getting straight answers.  Honestly, if there was any other option in town that would give me the service I need, I would have switched by now...but there isn't, so I can't.   Can anyone here tell me what any of these mean from the Cox perspective and what I need to try next before I pull my hair out???