I'm familiar with the oven method you describe. You often have to manually override the oven's default max, if you can, and set it for 500 degrees to begin.
I think it could be duplicated on the grill but would take more effort in both moving the meat farther away from heat after those first few minutes, and continually adjusting the grill to lower the temps.
What I don't know, about the oven method, is the rate at which the temp slides away. It takes a few hours to cook that way, so I imagine it's fairly gradual.
If she hasn't made that dish in a while, ask her to do it again, but place an oven thermometer inside, where you can see it through the window. Jot down that internal pit temp at various time points. When you do it outside, you'll have targets you know you need to meet for when adjusting the grill.
I would think something like a stacker that allowed for direct (but dispersed ...) heat (with the meat not in close proximity to coals )would work best?