I know a guy who had this issue back when both plants were legal. He told me that he changed one thing and everything improved. He decided that it was OK to swallow the juice and to not even try to stop it happening automatically. Pretty soon he completely forgot about trying to hold in the saliva and everything just went well after that (for both plants).
With Khat, he would swallow a shot of 'Juiced Tips' first, and then chew a bunch more soft tips for a couple hours, and then swallow some more 'Tips juice' a few hours later, and then keep chewing and keep repeating for hours. It takes an uncomfortably long time so you gotta find a comfortable way of chewing. Basically you gotta go all afternoon and night, which he said "pretty much sucked", but he loved the feeling.
With Sal, he'd prepare a scoob or two of simple dried leaf, chew as many leaves as he could for a while until he felt it start kicking in, and then light up with just a normal bic lighter and get as much of the scoob down as fast as possible. Usually by 80-90% of one scoob it was just right to let go and sink right into it and become one with nature like never before. "Most amazing feeling ever" he reckons, and "Best done in the evening or night with the soft golwing embers of a campfire". Apparantly it really helped with some crazy PTSD shit so it sounds like he had a totally positive experience. What a shame they banned it etc.