Oh, I would steer away from using quarter sawn white oak as a backing. Due to the ray fleck found in both white and red oak, these are MUCH more pronounced in quarter sawn lumber, and I've had quarter sawn white oak snap at very low poundages. But, where it fails in backing, it EXCELLS as belly wood.
If it were me, I would just reverse your order - Hard Maple back, Purpleheart core, and White Oak belly.
I'm not sure about the dimensions to get that high of a poundage, but when it comes to bowyery, it's all about EXPERIMENTATION... Start with one set up, if it blows up, or comes in at a different weight, try something different.
There CAN be a lot of math involved to try to figure this stuff out, but my methodology involved sawdust and splinters.
Start with 1/8" Hard Maple backing, 1/8" Purpleheart core, and 1/2" White Oak Belly.
Make your glue up 2" wide and glue in about 3" of reflex.
When that's dry, cut it at 1-1/2" wide until about midlimb, then taper to 1/2" nocks.