I did book a RTW trip with One World a couple of years ago. I agree it was not the easiest process, with constant backtracking in order to amend the itinerary if the dates/times did not work regarding my plans, particularly as I was being selective on the types of aircraft being operated. I also had difficulty in trying to get through to the right department at BA in order to pay as on One World you can book the flights but you have to ring the local airline at your starting point in order to pay.
In the end I am retired and had the time to do this, which otherwise an agent would do. I did eventually get it to work and enjoyed it, partly as going round westwards made the jet lag easier and I only had one overnight flight back from Singapore to LHR.
Hope that helps.