Going from Turtle Wax's red rubbing compound to their polishing compound is a huge step from a heavy abrasive to a light abrasive.
The fact that they don't use a diminishing abrasive in their compounds makes me turn away from using their products. (Diminishing abrasive: When the abrasive in the polish breaks down during buffing, turning into a smooth polish)
Turtle Wax rubbing compound stays abrasive throughout the buffing.
I'd use Meguiars Scratch X and an applicator pad to apply. Work it in well by hand using a good amount of pressure, you may need to do this more than one time, but it will work well.
Top shelf in the black tube here...