Grandparents (7) visiting first grand baby

Since I can't seem to find the rule book, has anyone had experience handling multiple sets of divorced and remarried parents... some of whom are less than friendly... and all 7 of whom are from out of state... visiting their first grand baby?

If they were all local I wouldn't worry as much, and would assume they'd all visit the hospital and schedule time to visit us at home periodically following her birth. However... given that they're all out of state, we're really struggling finding a way to give them all the opportunity to meet her immediately and also have alone time with us... all while allowing my husband and myself a little bonding time with the baby without branding myself the controlling she-devil wife.

We'd suggested staggering them all out week-by-week and my FIL and his future wife freaked out to have to wait. Of course they also got engaged 2 weeks ago, on the weekend of our baby shower, and just asked us if October worked for us to travel to their state for the wedding (we are due September 18th)... so we aren't dealing with the most understanding, selfless folks here.

Has anyone successfully managed a similar situation? Are we overthinking things? Hellllp 😬