I'll make a few comments since I live just 20 miles north of US 80 in East Texas (North of Longview).
We often choose to drive to Dallas using US 80 from Big Sandy, Texas instead of going on I-20. It is a far more peaceful drive and we make just as good time--especially with the trailer since we don't drive with it at 75 MPG anyway.
We are also familiar with US 80 to the Louisiana state line and use portions of it instead of I-20. We have never driven all the way across Louisiana on 80, but have driven portions of it--just for a different experience when we were not in a hurry.
We have driven several times from Columbus, GA through Montgomery, AL to near the Mississippi/Alabama line--both with trailer and with auto. A few times all the way from Macon, GA to that same place near Meridian, MS. Never any problems on any of the portions of 80 on which we have experience.
You mention US 380, so I will make some comments about that. A good many years ago our route to the West and Colorado was to go up to I-30 and take US 380 from Greenville, TX to Denton where we picked up US 287. In more recent years that portion of US 380 beginning around Farmersville, TX through Princeton and McKinney has become impossible for us because of traffic congestion and many traffic signals. We no longer go that route at all. We go on through Dallas, but more often go up to US 82 at Paris, Texas and then west. Of course that depends on where you are going west. If you want to go on west on US 380, I'd stay on 80 to DFW and pick up 380 west of Fort Worth. I 20 around south of Dallas/Fort Worth has never been a problem pulling the trailer. In fact, I've never had a slowdown. I know one wreck could change all that.
Let me know if you have any questions that I may be able to answer about the path of US 80, especially around here.