Those Turtle Wax compounds are highly abrasive and just don't work well by hand. They do a great job of removing severe defects, but it's like doing so with a coarse grit sandpaper.

If you pick some Meguiar's ScratchX 2.0 and apply it with a soft foam wax applicator pad it will take that haze right out. Piece of cake. No need to follow with anything but a good wax.

Keep in mind that even the highest quality wax alone will NOT remove the haze. A "pure" wax product (ie a non-cleaner wax) has zero ability to remove any sort of defect. Some may conceal very fine defects, but that's simply because you are apply a film of something to the surface and some concealment is bound to happen. But that isn't a fix for the problem.

Get the ScratchX 2.0 and toss that TW stuff.