As you've probably discovered from UA's award chart, you don't have enough for 5 roundtrip in Y much less F. You do have enough for 5 one-ways in Y, assuming Saver availability on UA.

With BA being distance based you'll pay more in mileage compared to others from the eastern US, but with the balance you would have it would get you 5 one-ways in Y on AA if available.

Your AA balance might help with part of your group.

UA, BA, and AA availability can all be easily checked and booked online. I certainly wouldn't waste money on an award booking service for it. They can't get you a lower mileage rate than what the published award rates are in any case.