Just a thought...when we moved right before Christmas two years ago, I ordered address labels from www.familylabels.com that said "A NEW HOME FOR THE HOLIDAYS" and then showed our names and new address. I used them for the Christmas cards and killed two birds with one stone (and one stamp!). You can also put a face on the labels (you have to see their labels for this to make sense), so we put a baby boy in a Santa hat for our son.
You could do "A NEW HOME FOR OUR NEW BABY" or something like that, use those labels on the envelopes, and then keep the birth announcements just about the baby and your family.
Again, just a thought...Congrats, good luck, and God bless!
Oh, and a lot of websites have pre-ordering for birth announcements - they'll send you the envelopes now so you can get them addressed, everything is ready for you to just send them the details when the baby is born...