Welcome to Flyertalk and welcome to the BA forum.
That's the morning A388 service, BA285. At the moment it is not sold out in WT, indeed has quite a few seats going at the moment. However it's a Friday by a holiday period, and on Fridays it is not at all unusual for BA to sell out every single seat to the USA. Also A380s have a reliability issue, so perhaps around 15 May you give this forum another ping just to check whether BA's stock of A380s is OK or not. BA has something known as Theoretical Seating (TS) so it is almost certain that BA will give you a block of 3 via that mechanism, particularly looking at loads and the arrangement of seating. So unless you really want a window seat I can see the point in not paying up and waiting to OLCI. So long as you don't download, App, print, email etc your boarding passes you can also move them after a few hours since the process is very dynamic and better options sometimes appear after everyone tries to move towards the front of the cabin. It's best to do this on the website rather than the BA app since it's very easy to accidentally download a boarding pass and then you're not able to change it.