Back when my children were little (most of them have children of their own now) their wonderful doctor told me, "You can't win food battles with your children! Don't get into battles that you can't win."
As long as your baby is healthy, I think you two are not having an eating issue. You're having a power issue. Swallowing is something your daughter, rather than you, has complete control of. She's not being naughty (per se). She's just being a tot, trying out something she has found she can do.
If she were really hungry, she'd be eating, new teeth or not. When she's not eating, she's not hungry, and the meal's over. Spitting out food (on purpose) is icky *and* not eating, so the meal is done. Don't lecture or wheedle or make any other big deal of it; just don't play the game. Keep your good humor but don't play.
This applies even if she doesn't get much food into her. You can always move up snack time if you find it necessary (but don't say anything to her about that).
When your girl realizes that the game isn't fun any more, she'll drop it (and look for something else to do - heh heh).