HaKatan:
1- The hhes (two h’s to differentiate from a hey and a chaf) is not a guttural. It is formed by the palate. Ahskenazim do have a mesorah for it. Check any ashkenazi dikduk sefer e.g. Minchas Shai.
2- Please explain your assertion that prounouncing a tav refuyah like a samekh is better than prounouncing it like a tes. (If you wanted to be super accurate, you would pronounce it like the “th” in bath)
3- You are only half-right about the kamatz. Real mizrahhi havaros differentiate between a kamatz gadhol and a kamatz katan but not between kamatz gadhol and patahh. Yemenites differentiate between both as do Ashkenaz-ashkenazim (yekkes).
Even closer than Teiman is Moroccan. Their havara is like the yemenite one except for three things:
1- a weaker arabic accent than the Yemenites
2- A gimmel degusha is notpronounced as J
3- Moroccans pronounce a quf with its own sound. Yemenites pronounce it like our gimmel.
The last two things on that list are things which Rabbenu Sa’adia Gaon said the Temanim do incorrectly.