You may find it helpful to arrange your pillows so that you sleep on your side rather than on your back. You might also try sleeping with your upper body propped-up. Keep a diary of foods you eat and medicines that you take. Then you can see if there is anything in common on the days this happens. Sometimes people become overly sensitive to what are normal amounts of saliva.
Since postnasal drip is a major cause of chronic, recurrent cough, you will need to have a thorough exam to be sure that you are experiencing excess salivation. The Modified Schirmer Test measures the amount of saliva produced. At the University of Indiana School of Dentistry this has been studied by Dr Fontana, Dr Zunt, Dr Eckert and Dr Zero.
are you sure it saliva and not mucus that could be caused by an allergy? I had similar problems that turned out to be a food allergy.
my allergy turned out to be to CORN. It's used as a thickener and sweetener (dextrose) in lots of processed foods. I woul dhave so much mucous flowing after eating pasta sauce that I'd be awajebed by choking every few minutes until about 3 am when the stuff finished digesting. it was terrifying. My post nasal drip has finally gone after at leat 10 years, only though avoiding corn.