You will certainly get full miles on a DONEx, be it QF or AA coded. Your agent is also correct that touching any continent, however briefly, counts. So it is a DONE4. There's no way to avoid flying through either Asia or Africa from SWP.

Fare quotes can take a few days, depending on whom you're dealing with. One DONE4 issue got me an almost instant fare quote (including taxes) from a TA, and the AA RTW desk often gets me a full quote within hours.