I tend to book 6 days out to as close in as the day of departure. I'm typically looking at either long haul C or F cabin bookings to AP or EU from the US or to Hawaii.

I'm usually booking *A using UA or US points.

That said I've done a number of CX tickets inside 48 hours prior to departure leveraging BA points.

So long as you are looking for not more than 2 seats on the same flights- finding space usually isn't a problem.

I have in the past booked our family of 4 to EU in biz day of departure with no return booking in hand - this was with OW. The return worked out - patience waiting out the airline to release seats was all that was required.

As a general rule I find airlines get very generous with releasing award seats closer in to departure - as they become confident of projected flight loads and premium cabin sales levels. For now this process worked reasonably well for me.