"The problem I see with it is that Stralman was also playing with a vastly superior defensive player than Klein was. Which, again, is just a part of a huge issue with any of these stats."
You don't trust the shot suppression measurements because Stralman had a better partner. I don't know what else to tell you other than to look at the adjusted stats. Stralman's not a product of Staal. Staal posted by far his best possession numbers in recent years playing with Stralman this season. Stralman posted a higher corsi than Staal in the playoffs, which means he was even better in his odd shifts away from Staal.
Look, you can buy the numbers or not buy the numbers. The advanced metrics do not make Klein look good no matter which way you look at them. They were bad when he was paired with John Moore and they were bad when he was on Nashville. If you really want the ins and outs of why this is, then ask Ail or Blue Blood. Or you could continue to assert that you've found the hole in the advanced stats that lets you ignore them and the fact that poor possession players make for poor possession teams, which do not win Stanley Cups.