FlyerTalk Evangelist
Join Date: Dec 2003
Location: Benicia, California, USA
Programs: AA PLT,AS,UA PP,J6,FB,EY,LH,SQ,HH Dmd,Hyatt Glbl,Marriott Plat,IHG Plat,Accor Gold
Posts: 10,820
The Honolulu call center tends to be the most competent and friendliest, and you're more likely to reach them in the evening mainland time, but there are no guarantees of doing so. Also, I'm not sure if it serves general members or just UA elites, and I don't know what your status is.
Awardnexus.com is a good service for finding award travel availability that you can then tell the customer service rep about. Given that UA sometimes blocks availability of awards on partner airlines (or at least I think it still does), what you see at that site isn't guaranteed to be available via UA awards, but it's worth trying. I think awardnexus is free for limited use by FT members.
Finally, I believe I've read here that going through CO reservations is much better than through UA, but haven't tried that myself.
Good luck!