Can't comment about UAL's policy. However, if he want's priority over CX aircraft declare an emergency; equally if I want one over him, I'll do likewise... worldwide standard.....
The only priority we seek is over fellow company aircraft. The request is placed by us well in advance and the Company will decide if they want to ask HKATC. If they are not prepared to ask; they let us know and we make appropriate plans. If it is HKATC policy not to not play this game; so be it; write to CX explaining such and we all know where we stand.
The few times I have seen this done (maybe 3 times in 6 years); it worked well.....