The tool slanting down slightly on the side to the chuck is not going to significantly impact the cut quality.
As BVD above said, the spindle speed when threading is critical. You want nice threads, use HSS and run the spindle as fast as you can control. Threads cut at 70 rpm are going to look terrible even if you get everything perfect and are using HSS.
HSS will work better at slow speeds than carbide, as carbide relies on speed and pressure to make the cut, and does not work well when cutting very small DOC. How much were you taking off on a pass when you were cutting the threads? Carbide does not like only taking off 0.005" at a pass, and will tend to skip across the surface, giving an irregular cut.
The close up of the tool you used looks like you are using a CNMG insert? You can't cut threads with that. You need a tool with a 60 degree point (CNMG diamond has an 80 degree point). A threading tool has a fairly sharp tip, the CNMG you are using has a fairly large radius on the tip (looked like a 1/32", like on a CNMG 332)
You said that you believed your setup was correct. Based upon what I have seen so far, I bet you have some other issues with your setup you haven't shown. Was your compound set at 29.5 degrees from the 90 degree point (depending on how your compound protector scale is labelled)? Did you feed with the compound while threading? How much of a cut did you feed each pass? What was your feed rate? What was your spindle speed?
By the way, I suspect the damage you showed on your carbide is because you were grinding rather than cutting. Small cuts are death to carbide, as you really need a good chip to remove the heat from the part. If you barely kiss the workpiece, you will end up eroding the tip of your carbide.
At the end you showed a 60 degree HSS you ground, which looks like it should work (although I couldn't see how much relief you ground into the tool based upon the video). Were your earlier threads with the carbide?
Here is great video on grinding a HSS threading tool (this guy was my instructor at one point):
https://www.youtube.com/watch?v=jnmFUBpmEF0&spfreload=10
He also has two previous videos on grinding a LH and RH tool bits.