Ok, lets say it is 15 meters, LOX with 1.1 g/ml and at acceleration of 5 g. This gives the pressure difference of 15*1.1*5 atm = 82 atm. This is the excess pressure in side buster tank which is required just to keep LOX from going backwards, from the core.

Wrong calculation. You forgot to multiply by 9.8 (g), multiply by 1000 (density is kg/m) and divide by 101000 (KiloPascals in atm).

Not 82, but around 8 atm.

82 atm (1200 psi) looks more like the pressure in the combustion chamber!

A ball valve is not needed. Think simpler! If you have two tanks feeding a burner, one your adding pressure (side boosters) and the other your not (center core) then the flow will come from the side tanks and not the center tank. When you need to switch to core flow you start to pressurize the center tank which will decrease flow from the sides to zero. Now you close the QDs to the boosters without interrupting flow to the core engines.

You will need a cut-off valves anyway. I do not know if it is easy to balance delicate pressure difference between tanks. Without 3-way valve the side boosters become also interconnected and can exchange fluid between them, so may be 3-way valve is simple enough to simplify control logic. We may learn what approach SpaceX selected closer to actual launch.

I'm sure Elon will take this opportunity to boast how unheavenly smart his team is!