I know exactly what you mean, I started having the exact same experiences a few years ago, not every night but every now & then. Finally I went to a doctor because I thought I was going to die from suffocation & he checked my breathing & everything was normal. He diagnosed it as an anxiety attack. At the time I was having family problems and it made a lot of sense. He also gave me book on panic attacks / anxiety disorders which helped a lot. It's all in your breathing. If you notice right now you're probably breathing high up in your chest?? Ever since this was pointed out I've changed my breathing & the attacks have stopped. Not sure if yours is the same thing but sounds very similar. Hope this helps.
Sometimes that happens to me a bit, but it usually is simply the result of a stuffy nose, and having my mouth closed and therefore not breathing full for a few breaths. In fact, I had nose surgery for a deviated septum, and during the healing process with the packs in place, while laying in the hospital bed, I suddenly gasped badly and told the nurse I felt like I couldn't breathe at all, expecting some kind of emergency code to be announced and having a staff of medics rush in, and she said simply "your mouth was closed, you have to remember to keep your mouth open to breathe."
That may not be your problem, but I mention it because, considering you had all the tests and doctors have said it's all normal, it is very possible that the cause is something as simplistic as nasal congestion or something like that. A habit of very shallow breathing will also exasterbate a breathless feeling as well.