I have been very lucky w the past couple rehabs. I soak the firebox interior, grates, etc. with a strong degreaser. After an hour or two, I fire up the Honda engine on the Ryobi 3000 psi pressure washer, attach the awesome turbo nozzle, and blast away until 90% of the crud is gone. Rinse and repeat if necessary. Any remaining few spots quickly come off with a touch of a coarse sanding sponge or the old cup brush.
And when not cleaning fireboxes and assorted parts (wheels, drip trays, durawood or wood slats, Weber badges, even lids), the p-washer cleans autos, windows, siding, concrete slabs, stone, screens, wood fencing, gutters etc. There are a myriad of "nozzles." IDK how I've lived without a p-washer all these years. It's probably the smarter investment for the handyman who also rehabs grills. IMHO.