Cathay does have a RTW desk that has been given high marks by those here who have used it. You can probably reach it through their US reservations number, (800) 233-2742.

I assume you have pointed out to BA that you are giving them a long haul segment and that they should, therefore, be more willing to ticket you.

As has been mentioned in other threads, there is no reason to fear a hand written ticket, although I'll admit that getting one from AA is now tougher that the RTW desk no longer can write them.