After weeks of attempting to defeat this boss at level 80, I decided to use the Maya glitch initially discovered by Shadowevil:
I had to modify his idea since the only character who was eligible for the boss quest was Gaige. It took 2 weeks to grind a Maya from level 1 to 80, and to get her into UVHM. But, this was a hidden blessing. Gaige was intentionally downed by a rocket inside the elevator. She was respawned inside the room with the Drop button. Both players do not need to be in the control room! In fact, player 2, 3 or 4 could also position themselves at strategic points, if desired. Maya could leisurely set up in the crater where Haderax spawns. She enters the crater from the slight V depression on the rim, and moves to the center. She looks up, as in the video, and sets up the aim for a Slagga (my weapon of choice). Rotate, if necessary to get a clear line of site into the sky. I found that a 90 degree (left) rotation of the field of view generates consistent results. The rest of the process is simple- no rushing to get to the crater, or positioning the shot. This is the number one problem with doing this solo, according to the comments. Just start firing when the music tells you that Haderax is entering the picture. A big red graphic label will also appear with Haderax’s health bar.
Since there are two level 80 players on the team, I was worried about Haderax’s HP being higher than the damage he would receive from Recompense. To compensate, I used a +28% SMG damage relic, but this is probably not necessary.