I'm confused because I thought originally you wanted a katakana rendering of those phrases, but in your post above you also have Japanese translations (the ones with the kanji in them).
The translations (the ones with kanji) are fine. Other options also exist;
梅花苑 Baika-en = Plum Blossom Estate (emphasis on the land)
梅花邸 Baika-tei = Plum Blossom Estate (emphasis on the building)
教区 is literally "parish", with religious connotations, and therefore is unusually specific in its application. If you are just looking for a municipal division without the religious connotation, you could use 群 (gun) or 町 (machi or chō), 村 (mura) etc.
Or just 区 (ku) without the 教 in front of it.
Violet blossom estate would be 紫花苑 (shika-en) etc...
To my mind these translations are better than long strings of katakana, which can become tedious to read, especially if the text will be repeated throughout the video or text that you are creating. On the other hand, if you want to replicate the sound of the phrase, then your only option is katakana. And, if your target audience is small children, katakana may be a better choice. If your target is high-school and above, kanji is fine.