Any of the old style anti-histamines (for allergy and travel sickness) cause dry mouth as part of their side effect profile (anti-cholinergics). It didn't work for Alex but maybe your pharmacist can help?

Unfortunately, nothing worked for Alex except time. We tried using agents to dry the mucous as well as agents to try and make it less stringy. I recorded how much mucous he had, how often he had to spit, how many times he had choked that day etc (drove him mad but but he humoured me).

The only thing that gave Alex some relief was clearing it out of his mouth manually. Swishing with the liquids recommended by others will help do this. The Water Pik was Alex's favourite and he still uses today as he gets "foam" now. Not as thick as what he first experienced but thick enough to get in the way of his speech at times and difficult to swallow effectively.