June is not yet loaded into the system. For a trial in May 15-29, the tickets are 1700$ each in AA for coach.
Here I would use 100k AA miles and go in Biz all the way.
Or use 100k miles each for family of 3-4, buy coach for me / 2 and upgrade with VIP as far in advance as possible.
If even considering coach all the way, then by all means use miles. Much cheaper.
Remember that to upgrade you have to
1 buy economy at 1500
2 spend 50k miles
3 spend 700$ =
Total value = 3000$ - for which I would just buy Biz.
Better to get C awards directly.