I'm not sure how the more experienced FlyerTalkers do it, but I just use the
Multiple Destination Flight Search page.
I just tried to book your itinerary for an early May departure and got a price of $1,412.60 all in S class for 18,575 PQM (that's 7.6cpm if I did my math correctly). You can get W class on UA metal for $1,798.60
The GCM looks like
this.