What is a 'small' amount of Tide Free? Could you not be using enough? Try increasing it a bit (or get a cloth diaper laundry soap-Country Save, Rockin Green or Charlie's soap).
If 'small' amount is plenty, maybe the two rinses still aren't getting the soap out (Tide is notorious for 'sticking' to cloth inserts) and you should use even less.
Add 1 cup of baking soda to you're cold wash and 1 cup of vinagar to your hot wash. Double stink control and since you are not adding them both at once (and they are rinsed once in between) the effects will not cancel each other out!
Clearly, as you can see, the wash process is trial and error until you get it figured out! LOL!
Make sure your inserts are REALLY dry when they come out of the dryer, if you leave them a little damp, it will cause them to smell as well.