Unless something has changed there are also EA moorings (about 3 or 4 narrowboats worth) above Abingdon lock. They're just past the waterpoint and pumpout. They are often full by late in the day, if not earlier, though.
If the OP's timings require/suit a stop at Abingdon then I would suggest starting to look for somewhere as soon as he leaves Culham lock. There are a few spaces on the left just up from Culham lock. There is also a very good wild mooring space opposite the entrance to Abingdon marina (or at least there was in 2018 when I made use of it). Once past the marina start looking for spaces on the R/H side opposite the almshouses, church and pub. Between the bridge and the lock there are numerous moorings on the right and several on the left at Abbey Meadows and the outdoor swimming pool. Beyond that there are a number of spaces on the right just before the lock.
All of these are popular but Richard (Abingdon lock keeper) has told me on more than one occasion that the river has been quieter ever since Covid so there might well be a space or two still available late in the day in August. If not, the river is wide enough for breasting up. I'd be surprised if it was not possible to find at least one narrowboater willing to allow someone arriving late in the day to do so, particularly if they intend setting off fairly sharpish the next morning. There's a large Waitrose nearby as well, useful if a bit of shopping is needed at that point in the trip.