I'd say Step 1 is figure out the personnel. Get guys off the PK who are struggling. At the very least, that means less Beecher and Hampus. Promote the guys who are doing well (Elias, Marchand, Zacha, maybe this is how Wotherspoon becomes a regular). Give Lohrei a shot at some PK time. Maybe that even helps improve his defensive play at ES.
Step 2 make the easy fixes, like clearing the puck when you have the chance. I've never seen so many failed clears. I wish more teams would lob pucks. You can't keep in a puck that's 20 feet over your head.
Step 3 is a tough one but your goalie has got to be your best penalty killer. Swayman is 73rd out 74 goalies in PK expected saves. That's horrendous. So, while it's kinda shitty to just say play better, he needs to play better.
Step 3b: The whole unit needs to play better. They choose not to engage guys in front so they can block shots and passes... ok, then block some freaking shots and seam passes. Carlo got beat twice on a goal last night, once in front and once behind. Get your sticks in passing lanes, get your bodies in shooting lanes... The habits suck right now. Play better!