That's not how RM/IM algorithms work.
Try pricing 1 ticket, then 2 tickets, then 3 and so on, until you hit a break point. Book that number and you will have the lowest price possible for that many tickets. Then start again and book as many as you can at the next highest price and so on.
Doubtful that group pricing helps you hear as you are close enough in that the names of the travelers ought to be set and you likely don't now need flexibility.
One thing I would not do is delay. No idea what carrier or where you are headed, but the last few seats on almost any aircraft are going to b e eye-poppingly expensive.