Ill ask again in the valve sized right. I have seen elevators start running up as soon as Y comes in when someone has turned Bypass instead or relief. If your valve is sized correctly then it a matter of trouble shooting and find out why Up and high speed are picking before doors and gates are closed. If it only does it in one direction then your problem lies on the up side of the circuit.
I take it you mean even the bypass pressure is good enough to push oil to ram and lift the elevator? My problem with that is, the Y shouldn't even be engaging until the doors shut. The motor shouldn't be attempting anything at that point.
