This probably isn't the problem...however...the cable routing at the cinch bolt (nut, really) on the derailer is not how Shimano intended it. The cable should run straight...from where it exits the cable stop at the back of the derailer, straight through next to the cinch stud-and-nut, and then straight out the front. I'd think this would primarly impact shift indexing, if it impacts anything at all, but I thought I'd mention it anyway.
So it's basically ghost-shifting under load, right? Ghost-shifting to the next smaller sprocket? Things like this that happen only in certain sprockets are usually attributed to something like uneven wear on the cassette, or improper alignment of the derailer. That said, 7-speed drivetrains are generally pretty easy to adjust and forgiving of stuff like this. I might tighten the barrel adjuster just a little bit to bias the derailer just slightly inward on each sprocket...almost enough to where it wants to downshift to a larger sprocket on its own, but not quite. This may prevent the chain trying to walk down to the next smaller sprocket on its own.
I suppose a left-field answer might be to check the frame carefully for cracks or a weak weld. It's possible, though unlikely, that there's enough twist imparted into the frame while under load that geometry of the rear triangle is tweaked just enough to perhaps loosen cable tension of the shift cable momentarily. It doesn't appear that the plastic cable end of the rear derailer cable loop is sitting squarely in that seat stay cable stop. I wonder if there's any unwanted movement there. Again, probably grasping at straws with these last few ideas...!