On the bright side, there are so many teams that already have no hope this year that I think trades will start to happen in late May / early June. Oakland has some targets other than Miller that should come cheaper (I really like Erceg from that group). There aren't as many obvious options on other teams, but Colorado, the White Sox, the Marlins, and Angels are already down to a near zero percent chance of making the playoffs.
I'm actually hoping Washington craters over the next month. I'd love to target Hunter Harvey as someone that could help this year and next. He's not a "closer", so he'd come a bit cheaper. But he throws a ton of strikes, throws hard, and gets whiffs. He's even been a ground ball monster so far this year, too.