Try to stabilize a dream and ignore the sensations of your real body. If your brain is processing "I feel as though I am laying in a bed in my bedroom" I think you're going to have trouble simultaneously experiencing "I feel as though I am flying through the air/doing battle with dragons/having dream sex/driving a sports car/whatever". Whenever I pay attention to my real body in dreams, the quality abruptly ends and I typically wake up

Just ignore it, and overrun whatever you just experienced with dream sensations. If you can hear your fan, imagine you hear a DC talking to you in the dream and focus on that (of course, sound is different). If you feel your pillow on your head, imagine it's because you're wearing a helmet or hat of some sort is my advice.