The question is, Does the speaker (writer) need to use "got made" to mean "arranged for someone to make" when, as in a written text, there is a possibility that the reader could mistake "had made" for past perfect.
In spoken English, these two typographically identical sentences would have different "parsing rhythms":
The thorn bush tore the dress which she had made. [she made the dress herself]
The thorn bush tore the dress which she had made. [a seamstress made the dress for her]
When had is an auxiliary verb, as in the first sentence, there is very little pause between it and the lexical verb and between it and she. In fact, you will often seen it contracted: ".... which she'd made".
When had is a lexical verb, as in the second sentence, where it means "to cause or to arrange for someone to perform a task on your behalf", there is not only a much greater pause between she and had and between had and made, the vowel in the word had will also have a longer duration, equal in length to the vowel in made. had made would be a spondee.
Spoken by a native speaker, the two sentences would sound quite different.
In writing, if you wanted to make clear that you had the second meaning in mind, you could add "for her".
The thorn bush tore the dress which she had made for her.
although that is not perfectly clear, because we don't know if her refers to herself or to another person. (Context might clear that ambiguity up.) It would be clearer to say:
The thorn bush tore the dress which she had a seamstress make for her.
But context will normally support the less explicit version. Context will tell us whether there is a third woman involved, she, the seamstress, and the person for whom the dress was made.