The UV layout for this model makes selecting rows very easy with the Box Select tool. (I hid the ends because they have hidden faces that are causing problems.)
By selecting every second loop of the UV's and then using Tris To Quads, you can establish guide loops that allow you to use the tool again and achieve consistent results.
b for Box-Select. Also make sure to activate the icon for use_uv_select_sync as shown in the animation.
Now use Tris to Quads on the selected rows, then select everything and repeat Tris To Quads.
Now you can repair the few mistakes by using the Join tool j. In the following case, I used Join and then used Make Face f to make a quad at the center of the error point.