Alcohol can inflame your gums which can lead to gum disease. Best to use non alcohol versions.

Rinse your mouth with salt-water. It's cheaper and more effective!

Whats your diet? I'm not trying to ignite the traditional HN flamewar about the evils of a science based paleo diet, but I have had a similar experience where not eating grains or sugar none the less results in a relatively tartar free mouth per my dentist. Even though I hate waiting and am impatient and do not visit every 3 months or whatever often its supposed to be.

Archeologically, before people started eating grains and processed "psuedo-food" we mostly died with good teeth and its a stereotypical observation that you can tell when grain agriculture sets in with a people when their teeth start rotting out at a young age.

My understanding from what dentists have said to me in the past is that ordinary toothpaste in the abstract is of limited value, especially if you brush often, but it's a useful vehicle for fluoride.