Simple. You pick your core guys and try to re-sign them early. If they're not going to re-sign for a reasonable rate, trade them while on their rookie contracts to teams needing that position, and recoup draft picks. Rinse. Repeat.
The good part about everyone peaking at once is that they will all _know_ that they're leaving something special, something capable of becoming a dynasty once it all clicks … well at least during the peaks of their careers. So, hopefully that's when guys will be willing to accept less to stay in Miami. If we're winning, Miami is an easy sell, great weather, no state income taxes, wonderful for kids/wives/girlfriends, and you can do whatever you want. Lots of NFL players have their homes in the area that play for other teams. So, there will be a lot of incentives to stay in Miami if we're winning and ascending.
Will there be guys who want to cash in, ala Jarvis Landry, sure, and let them. But we want to trade them rather than let them go and work towards a 3rd round compensatory pick. When lots are coming up at once, it's easier to tell one that you'll just sign the other guy if he doesn't take a deal early. We can't keep them all, but if you look at our history, there's a real track record of guys being draft as Dolphins, then thinking they're awesome and leaving to become nobodys on other teams and often not even seeing out that next contract because they're found to be less talented than people thought they were when they played in Miami.
But if having that many talented guys on the team at once gives us a sniff at a Super Bowl or three, I'm all-in.