Perhaps getting the yeast issue taken care of will fix the gum problem. I say tackle the yeast first.
I don't recall if you have tried to tackle the yeast problem with dietary changes.......... seems like you have. I know there is entire protocol on killing candida overgrowth. This looks like a good protocol to me. Try to trace back to when you had the yeast thing under control - what were you eating at that time? Has it changed since? Have you been eating more fruits or refined sugars? You may have to maintain a very low sugar diet - natural or otherwise to control the yeast overgrowth that you seem to be prone to developing.
The gum problem sounds horrible.......... I hope you can find something to bring that under control soon.