I feel it should be said regarding Ullmark - the last time the Bruins had a Vezina winner under contract for $5m was Timmy over a decade ago. That's rewinding a lot of time and a lot of cap increases.
While his value compared to Ullmark is tough to peg, it's indisputable that Swayman would have more suitors if shopped. Theoretically, he'd get them the Schneider return, a top 10 pick. Trading Ullmark won't save them appreciably more, as Swayman's getting ~$4m on a bridge deal and Bussi likely fills the backup spot with an ELC (less savings if they don't think Bussi's ready).
Ullmark was so good this past season, I'm inclined to ignore playoff failure and keep him. They might get a killer return on Swayman. The team really isn't expected to be overly successful going forward, especially after their latest enormity vs the Panthers. And we've got ample evidence of the odd goalie going nuts in the spring and dragging his team along. And there's really nothing about Ullmark that would make you certain he's incapable, aside from a small sample of playoff games.
Plus, he's a pretty cool dude.