Do you know if you're having a boy or a girl? Do you already have the "newborn" things you need for the baby, which ever gender it is? If so, why not wait until the baby is 6 or 8 weeks old and have a "meet the baby" shower. This will encourage your guest to bring slightly older baby gifts. (not so much 0-3 clothes, towels, layettes...) You could then easily have it at someplace like Mimi's Cafe (that usually have provate rooms) or Soup Plantation, Sizzler's... Where ever you preffer. Just be sure Dad(s) are willing to babysit the rest of the kids. (Your own and your guests.)
Or... I also read somewhere on this site about one of the Mom's had a "Big brother/Sister Party" and made it about their kids getting "big brother/Sister gifts" and had a huge jump house. I have thought about possiblily doing this if we ever get preg again.
You may even be able to do both... Dad has an at home party for him, the Dads, and all the other kids. You, the gals, and the baby can go out. (or EVEN... meet at the house so the gals can meet the baby, then go to the spa and leave the Dads in charge of all of them.) :O)
What ever you choose, enjoy your party and your new addition~ J.