It isn't really necessary to get your center under the uke's center of gravity to make koshi waza.
If uke's balance is broken, the next thing that happens is they either recover their balance or fall. As they try to recover balance tori fits their body to the uke's recovery cycle (keeping the balance broken) so that the hip is taking up space necessary for the uke's recovery. As uke's body just begins to touch tori's hip (even if it is above their center) tori continues turning (keeping close connection) so that uke's leg must thrust causing them to go around the impediment (tori's hip) launching uke into the fall. All you are doing in essence is causing uke to "trip" over/around the tori's hip.
There should be no "lifting" of the hips at all. A tiny sideways motion of the hips is often enough.