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You only need a one-way flight?

You would be flying British Airways metal and they have plenty of award space.

I would recommend booking as soon as you know what dates you can get away.

There looks to be a decent amount of award space early in the work week throughout October.

Remember you will be paying ~$300 each for your rewards flight.

You could wait but there is no guarantee any more award space will open on YOUR desired dates. In fact every day but yours could get award space and you would be no better off.

It is just a risk that you have to decide to take.

This close to the date of departure I would think flexibility is a virtue.

Good Luck on your award search.