Removing all that black pigment from your hair is going to be a potentially damaging process, so if your hair is "over-processed"; i. The primary tone in the colours you've selected is gold, and the secondary tone is violet. Caution, 40 volume developer is a whopper, as you've experienced with the bleaching, and is not something to be toyed with if you don't really need that kind of power!
The only real alternative is a wig. Put on your processing cap. I bleached my hair yesterday again and its orange and some of my roots are still black cause did myself and I guess I couldn't see every spot. The greatest thing about this cut is its versatility to be able to style in different ways.
Would just like to get her to brown and lighten over time, at the minute she has about 3 inches of strawberry blonde her natural colour roots.