How can I salvage burned apple crumble?
That is such a shame, they looked wonderful. 

You may well be able to save the not-so-burnt ones. But you'll have to check the burnt taste hasn't tainted the apple base.

I'd start by carefully removing the burnt bits, (as Dorothy suggested above) and inspecting / tasting the base.

To repair the crumble topping. Mix up a new batch and bake it on it's own. Then when it has cooled enough to handle brake it up and re-top the crumbles.

Rather than grilling/broiling you can get a small blow torch like the ones plumbers use. They are great for this and Creme Brulee. You have much more control.