Good information. But why are they fighting the fire from the back of the ship to the front and allowing it to spread?
I doubt they are “allowing it to spread”. There are a lot of very large open spaces on LHA/LHD class ships, including the hangar and the well deck/vehicle ramps/platforms, that make it very hard to set boundaries if the fire is in those spaces. During maintenance periods there are also typically large ventilation hoses and air/power/welding leads, etc running down long passageways that prevent boundaries being set. I don’t know what was involved in the F-35 modification, but significant reinforcement of the flight deck could mean firemain systems were cut, rerouted, or in some state of non-operation.
Once firefighting team evacuated, the ship was in serious trouble. Fighting a shipboard fire from a tug is not very effective. You need teams onboard. If you have a fire in your kitchen, and can only spray water from the street, you are probably going to lose your home.
From the videos I've seen, it look like the fire-fighting boats are try to keep the hull cool so as not ignite other internal flammables. Heat radiation is the enemy of any shipboard fire. Just my guess.