Unarmed attacks scale off of DEX only if your DEX is higher than your STR. If STR is higher or equal, unarmed attacks will scale off of STR.
The Tavern Brawler feat states that it adds double your STR modifier to your unarmed attacks. This is true even if you are using DEX for unarmed attacks.
If your STR modifier is 0 or less, Tavern Brawler adds nothing aside from the +1 to your STR or DEX.
In short, Tavern Brawler is a good choice only if you are building STR.
Your best bet is just to go with Ability Improvement to increase your DEX to 20.
I might also choose a feat that takes advantage of Monk's mobility, such as Mobile.
Other good choices would be Resilient to add Wisdom saving throw proficiency, or Mage Slayer.