My postmistress told me there's no way to avoid conver-belt handling, where you packages will be dropped 3 feet from one belt to another. The only time "Fragile" "this end up" etc. have any impact at all, is during short periods when people actually handle it. So I put on all the markings, and have added "Live embryos, handle with care!" and put cute pics of the eggs, babies of the species being shipped, and what they look like as adults. So far, the packages are arriving in good shape, one customer told me her carrier really enjoyed the pictures.
I think most postal workers would be careful with them, but the conveyor belts are the problem. There's no way around them. And, if they go by air at all, which they almost always do if it's very far, then they're handled by airline personnel, the PO has no control over that part at all.
So pack your eggs well, so they ride in the center of the box, away from top, bottom, and sides, and so they don't rattle around in the box. Then cross your fingers and hope for the best. I'm thinking M-T-W shipping may also be a good idea, as some of the other posters have mentioned.