Part of it is going to be their ages. They are just so excited and the impulse control isn't there yet. I can share what worked for me with my dog.
I greet very quietly and calmly: "Hi, Dog'sname." Then I'd remind her, "Four paws" (or "off" or whatever your command is - I don't use "down" because that means something different in our dictionary). If she kept four on the floor, she'd get calm praise for, "Good four paws. Good girl" and I'd keep petting her. If she jumped, I'd turn and hip check and say firmly, "FOUR PAWS." Lather, rinse, repeat. That's all it took for me, with a healthy amount of patience; she learned very fast what I wanted but actually following through was harder for an excited puppy. I like the idea of replacing the behavior with a "sit" in general, but I didn't mind her dancing around me as long as she wasn't jumping, and it was easier for her to just remember not to jump than it was to sit when she was so excited. (Keep in mind she was about 3-4 months old when I was doing this work, and she knew "sit" but it was SO HARD TO SIT STILL when The Human came home.)
The key is to not make it a party when you come home/in/over to them. You're happy to see them, who wouldn't be, but it isn't a dance party with a mosh pit.