High season, last minute booking. Challenging, to say the least.

On AA, by using AAnytime awards on AA, you have access to seats as long as they're available for sale. A suboptimal use of your miles, but this late in the game it may be your opportunity. But check for other options, such as partner airlines airberlin, Iberia, etc. (Avoid BA unless you don't mind paying hundreds of dollars per person for their infamous surcharges.)

You have three "currencies" to spend so look at one way awards using one, return using another. It's not going to be easy this late in the game, but good luck.