At this point if you add a closer and a backup 1B, this team is plausibly complete. Closer will likely take low 8 figures, and the 1B can vary (at the low end there are always Garret Cooper types available).
So I suspect that we see a closer added very soon here, and then Jed can just be opportunistic for whatever scenario presents itself as the best way to spend the remaining ~$20M. Flaherty? Awesome. Two closers? Great! Max Scherzer? It's worth a shot!
I'd guess this ties into Bregman. Bregman is the best player still available by a healthy margin. He also, at a likely ~$30M salary, does not fit as cleanly into the team's budget as other options. So I would guess Heyman is not making things up, but in practice this is Jed and Boras trying to nail down with certainty that Bregman to the Cubs won't work so that both sides can move on.