Hi Treefrog, I'm on the Cambridge diet and I have been chewing Ice extra sugarfree gum from week 3 - without it I think I would have given up yonks ago... for me it has not hindered my weight loss (or if it has I am totally unaware of it), however, my Counsellor did warn me that it might and if I wanted to try then it was up to me, I tried, and here I am, 17 weeks and 6 stone lighter later.. still chewing.. still losing.. and still smiling!
CD and LL may be totally different, ask your LL counsellor and whatever they tell you, that's what you should do. I may just be very lucky!

Hope you find a solution - I know its daft, but what about chewing a baby's silicone dummy teat? (I know.. it sounds mad.. but at least you can chew that way!)