But but but...
Not under 1mm pitch bga I hope?
Put in biggest possible cap = 0402
For 0402 thar would be 4.7u 6.3V X5R
Or 1u X7R, mostly for temperature range is better.
Probably 4V will be even better.
Forget the historical nonsense about mixed values.
Put your 1n, 10n, 100n in the trash bin where they belong.
Low esr, low inductance, big as possible values.
Never worse than X5R dielectric.
Avoid anything but ceramics.
Shouldn't really be any need for anything else.
I don't know why you had to battle for backside of bga caps.
It's industry standard, the big guys do it also.
It doesn't matter much where you place the caps for decoupling if your stackup and planes are in order.
But the real estate under the bga is free.
Also the vias are already there.
And yes, vias do cost money, not much of course, but why would you not use both the space and vias as they are already there.
Big gains even for resistors, yo be able to connect directly beneath and avoid a cumbersome fan out