how do you turn the overfow drain in tub upside down
I could be wrong but If read this correctly, it is not a case of it not working properly, it is a case of the water level in the tub being to shallow ( reaching the overflow before it covers her toes.) As lover of soaking in a tub i sympathize with her and wish for her to have a deep soaking tub, but short of a new tub there is not much one can do. 

I believe she is asking how to change the Height of the overflow opening to allow the water level in the tub to be deeper. 

The opening is on the underside of the chrome overflow escutcheon, You could try and take off the escutcheon,  put a wash cloth over the drain so you do not drop the screws down the drain. (three screws, two for the cover one for the handle, take the handle of first then take the escutcheon cover off) turn the escutcheon 180 degrees so that the opening is on top. you would have to caulk around the bottom. This would result in gain of maybe in inch and half of water depth. 

what i do is, when the water reaches the overflow i cover the overflow with plastic kitchen wrap, the suction will pull the plastic tight to the opening. This will buy you some time.  but you must not do this and walk away from the tub while the water is on. I an not responsible for any water damage that you cause. i will take credit for your happy toes.