No wrong answer, but no easy answer. Also, I've written this three times over, and I keep coming across like an a-hole; I promise that's not my intent. I want to contribute, I'm a genuinely nice guy, it's just late and I'm inarticulate...but here it goes...
Answering this from an F-Class perspective; if we're talking hunting guns etc. that's a different story. Also operating on the assumption that you don't want answers to include range conditions/wind as a contributing factor.
That said, I think I know the answers you're looking for, but I also think the scenario is a bit flawed. I don't see that there's enough info to give a full & complete answer. For example, 3-4 bullet diameters wide at 100 yards is a non-starter; at 400 and beyond it's probably something you could work with. Need to know what caliber we're talking about too.
First, the person in this scenario never had a "great load" to begin with. They had a load with flat vertical and good chronograph numbers, but that was all it ever was. To call it a "good load" would imply it was grouping well, and doing it with relative consistency (sounds like it wasn't).
If it ever shot well, I'd be looking at tuner (assuming it's equipped, because that's easiest to test), depth, and then tension (in that order). If those failed, I'd be going back to the last point where I had confidence and working from there.
The scenario also kind of paints you into a corner. Is the gun throated for this bullet and you have 3,000 of them just for this barrel? An "it's going to work" type thing? How many powders were tried before settling on this one? How many primers? I usually don't find myself in the scenario described because I try to cast a wide net very early by testing 2-5 powders and 2x primers during the first 100 rounds; it usually becomes really obvious what combo is going to work well. I suspect that eliminates 90% of what is described in the scenario.
I would also perceive the chronograph data as irrelevant (outside of knowing if you're going 2000fps or 2800fps) until you get your mean radius relatively tight, and a consistent POI. Once you've got those two things, I think that's when you can actually start to tweak a load to make it accurate.
In summary, I probably wouldn't find myself in this situation, because the person in the scenario is backed into a corner, trying to force a combo to work. If I did find myself in that scenario I'd have a new barrel spun up if I couldn't sort it out really quickly, because components are way more costly (and now significantly more rare) than a $600-800 barrel job.
Signed,
Not a-hole Mike