Hi, I just registered so I'm new to this forum but I have been mewing (or, for the most time, at least trying to do so) for almost a year. 

I'd suggest using normal (soft) chewing gum. Tongue chewing is way harder than regular chewing so you won't need - and probably also not be able to tongue chew - hard gum like mastiha. The small sugar content isn't gonna kill you but if you really wanna avoid it I would use plain gum base. You can even make your own sugar-free chewing gum with it. Much better than regular sugar-free products as the artificial sweeteners in it are far more unhealthy than sugar. 

I hope I could help. Btw, as a newbie, how do I post something in this forum? I couldn't find out how. 

EDIT: I have found out how to post now. 

No need for sugar in your gum. Most quality gums these days have xylitol, and that's actually good for your teeth. I chew Pur brand but there are others. You definitely want a relatively soft gum for tongue chewing.