I would use this pitcher exactly as a closer. Not as an important reliever. My best relievers are set SuA. I don't want to waste their innings in the bottom of the 9th, they get the 7th and 8th.
What I've been saying is that he's only having good results because his usage is highly limited, as it is in the case of a dedicated closer. He's coming in with no one on base and only needs to get three outs. Yes if he comes in against the top half of a good team's lineup, odds are he gets hit hard. Against the bottom half of a poor team's lineup he's good enough.
I'm, for the most part, a cheap closer guy. Think Fernando Rodney. A hide-your-eyes pitcher who got a lot of saves, because closing isn't a high leverage job most of the time.
Let me be clear: I'm not at all saying go out and find a guy like this. I'm saying if you're stuck with one, this is the way to get some kind of useful result out of him.