Hi there, rather than using the Turbulent Displacement effect, which is usually good but doesn't give you the looping options you are after, you can use a Fractal Noise effect & animate the Evolution value. In the 'Evolution options' you can set this to 'Cycle evolutions'.
I'd recommend creating this in a solid layer.
Then create your text and add a 'Displacement Map' effect to it and use your solid layer as a 'Map Layer.' (make sure you set it to Effects & Masks otherwise it will look at the layer prior to the effect you have added.) This will displace your text in a loop.
Now if you only want part of your text to be displaced then create a mask on the solid layer and add some feather to it. Only the area with the mask will be displaced and the area outside of the mask will remain un affected.
If you need more info I have a project file I can send you with this set up.