Try a Christian interpretation (although I'm not Christian): the "exquisite dead guy" is Christ. He's on display in all the churches, and it wouldn't be too far a stretch to have an image of Christ rotating in a display case somewhere. The singer is imagining that Christ is appearing to him in unusual ways: he thinks that Christ is talking to him, and sees him floating in the air outside his apartment building. He imagines he hears Christ asking him, "How am I supposed to let you know the way I feel about you?", i.e. "I've been trying for centuries to tell you that I love you, but you people won't listen."
Try a Christian interpretation (although I'm not Christian): the "exquisite dead guy" is Christ. He's on display in all the churches, and it wouldn't be too far a stretch to have an image of Christ rotating in a display case somewhere. The singer is imagining that Christ is appearing to him in unusual ways: he thinks that Christ is talking to him, and sees him floating in the air outside his apartment building. He imagines he hears Christ asking him, "How am I supposed to let you know the way I feel about you?", i.e. "I've been trying for centuries to tell you that I love you, but you people won't listen."