When you swallow the phlegm, your episodes are more likely to be prolonged because having phlegm in your stomach can promote reflux. I would recommend prevention first (e.g. avoiding dairy at night, eating slowly, drinking after each bite, keeping well-hydrated, etc.). Then I'd consider a suction machine (much less costly than a Cough Assist) so you can get rid of the phlegm after you cough it up. At least hold a folded half-paper towel to your mouth (we go through mountains of Select a Size towels) when you hawk/cough to capture what you can.
Tweaking heated humidification on your BiPAP and avoiding aggressive climate control and other drying environments is another preventive measure. Also, you might try papaya tablets, pineapple and/or lemon drinks and hot tea throughout the day.
It has helped my husband to "spit" (as he calls it) the phlegm into a paper towel every morning first thing and last thing at night.