[Buteo]

Painful mistakes happen.
I kick myself at least once everyday because I allowed "Milkshake", a young not fully fledged Northern Cardinal that we were trying to raise, to have full access to the outside. It wasn't my idea- I would have preferred to wait till it's flying skills were better before I released it, but the Cardinal is a native North American bird & I had to follow the letter of the law. The bird always had to have free access to leave whenever it wanted.
That fateful day, Milkshake had gone over the fence & was exploring garden in the next-door-neighbor's yard. Tragically, poor little Milkshake was accidently crushed underfoot in some long grass by one of the guys shingling the neighbor's roof when he decended a ladder.

Don't give up looking.....
and for your other Fids sake, please don't rehome them....
I understand it's a very common kneejerk type reaction to the emotional pain, but I think you'd find afterward that it would be a case of "throwing the baby out with the bathwater" and you would end up hurting yourself worse in the long run.

Lilly & Matilda won't understand why if you did,
but they'll sure help you heal.

As the others have said, posters/flyers & ads posted around might help.

Hopes & prayers are with you for Poppy's safe return.