Why would he want to move mid-season? The last thing I’d want to do is set up house again after spring training and moving for the regular season.
I think he'd probably prefer to have one place with a pre-season contender. I think the only way the Nats could have competed for him was to offer a better offer (a player option for a second year, or more money) and then said that the pain of being flipped mid-season isn't much of a detraction from the offer.
If it is true that Gallo was always Plan B after Plan A - sign Jeimer failed, then I'm guessing Rizzo never thought that a Rosario / Pederson / Belt / Votto was worth the premium. Maybe they did have Pederson as a Plan C and were seeing who took their offer first, Gallo or Pederson at a lower amount than $12.5 million. Could explain Gallo signing before Pederson.