Oh I think yours is totally fine and appropriate.
I, on the other hand, will probably do something like this:
"Hi, everyone! You know, we are so sorry that we forgot to send a personal message to everyone to let you know individually that we already had our baby, won the lottery, and have moved to a tropical island thousands of miles away. Life just happens so fast!"
Or something else really snarky!
Mama to 2 little darling squooshy faces