You can justify this any number of ways. It's still a rationalization. You don't trade away 25-year old 5-win position players. If you have to overpay them, you overpay them. They're paying BJ Upton, Chris Johnson, and Craig Kimbrel $72 million in 2015/16.
You start with the cornerstones (even if you have to overpay them) and then fit the rest of the team around your budget, not vice versa.
If you project Heyward to by a 4.5 win player through age 28 and then have a normal aging curve (losing .5 wins a year), and you project free agency values to be $6 million this year and to increase by 5% a year (conservative for recent years), then I get Heyward's extension value, including the $9 million he's making this year, to be 9 years/$217 million.
I don't think he was asking for anything close to that. If they could have gotten him for 9/$150 million or whatever, there's just not a lot of risk there. Certainly no more than spending the equivalent amount of money every year on Chris Johnsons, Ervin Santanas, BJ Uptons, etc.