No to the methodology question
Book the outbound then you need to call up to add the return. You can't book a return one way then join it to the original flights.
Three things:
(1) You may well need to be up in the middle of the night to grab the outbound seats online for busy routes.
(2) You will need to call up to add the return. Check for availability online then call up whichever BAEC call centre is open at the time. Not always advisable to wait for UK to open.
(3) If you have to be back in 20 days I would try for 18, 19, 20 days just to be sure. You don't want to only aim for a precise date and miss out. When I booked for HKG I had a +1 and -1 day in mind too. Track availability in the few days (or more) ahead too.