Do not use the sprays go and get a packet of mouth freshener strips as they don't knock you off ketosis. What I used to do with them is cut them in half just so they lasted a bit longer, aswell as became an obsessive at brushing my teeth till I was told by my dentist that I should either stop brushing so often or switch to using a baby soft tooth brush and baby tooth paste so I don't murder my teeth.
Drinking a hot cup of plain water before and after a shake does help the mouth area aswell as the dumping department.
ps the furry mouth syndrome will last about 2 to 5/6 weeks, just hang on in there and with some people it only lasted 10days.
Good Luck with your journey to being a healthy being and if you have any questions just ask