Bryce does not strike me as risk averse, and he has plenty guaranteed already to mitigate the risk even more. If he's not in the 1% for life with his first contract, he's darn close to it. I don't think he'd see an early signing at some sort of discount as a good tradeoff because he believes he will stay healthy and will be able to make more money later.
The best case for the Nats would be if he likes it here. There is something to comfort. If Zimmerman and Strasburg, Gonzalez and Zimmermann are still here for a few year after he hits free agency, the Nats are winning, it is fun, then maybe he'll not want to break up a good thing and give us a few extra years before he hits 29 or 30. The fact that he used to fitting in and playing with different players since his travel days probably works against this. He'll have buddies whereever he goes.
Watch out for the Dodgers if he hits free agency. lots of money, prime market, historic franchise, and close enough to Las Vegas and family to day trip on an off day.