I have a fancy to use the following approach in the analysis of an historical text:
The text uses a certain unusual expression that might mean a certain thing (or concept). The expression used is not otherwise attested to, and there are other well-attested-to expressions to say the same thing. My idea is to argue that if the author(s) would have wanted to mean that certain thing (or concept), they would have used one of the other, more common expressions to say it. The fact that they used a more obscure formulation indicates that they must have meant something else, since they would have used one of the common ones instead if they meant that certain thing or concept.
To me, this seems a common-sense approach, but what do I know. Is this an acceptable line of reasoning, and would there be any source that advises this line of reasoning in textual analysis, or makes use of it?
Is this an acceptable line of reasoning [?]
Acceptable as in logical? Yes. Correct? Not necessarily. Dozens of other reasons exist which could also explain it. It could just be a random thing with no meaning, translation could be getting in the way, the poetic inclinations of the speaker/writer, common within a niche context otherwise lost to history, etc. The list goes on.
any source that advises this line of reasoning in textual analysis, or makes use of it?
These sorts of source analysis is more common in Classics, the various subfields previously called Oriental Studies/Orientalists (although the successor to the Orientalists, Area Studies, often has less interest in it), and other fields with heavy philology connections. Most historians, especially modern historians, lack deep philological training (in general, philology as a subject has suffered a lot over the past century). I could offer some recommendations for the Orientalist examples, but to offer recommendations more effectively: what particular is your example in relation to? And is there a translation happening too?
Your suggestion can be a valid method of analysis, often used by linguists and literary critics rather than by historians, although a knowledge of both can be helpful depending on what you're analysing. It can often be found in translations or explorations of primary sources, I can think of many footnotes in Michael Swantons's translation of the Anglo-Saxon Chronicles for example which discuss the exact meaning of a phrase in its historical context and the significance that that brings to the chronicle. I suggest learning a little about sociolinguistics and corpus linguistics as these are lenses which would support your method of analysis, as below. Sociolinguistics is the study of how language is used by people and how society shapes language, so would support analysis of why that particular phrase was used above another, or what the cultural meaning of the phrase might have been. Corpus linguistics is the study of chunks of language used in its natural state to infer generalisations about language. Therefore it may be useful to study: other texts by the same author; texts about the same topic; other texts written at the same time etc in order to ascertain how common this phrase was compared to other phrases with the same nominal meaning. An example of this approach would be Dan McIntyre and Brian Walker's work on Early Modern news. Finally stylistics is the study of the style of language and what contexts it's used in, which works well with both sociolinguistics and corpus linguistics. This would support analysis of the social tone of the phrase you're interested in, e.g. if it's used more commonly in casual contexts or if it's a more formal phrase than what would be suggested by the rest of the text. Without the full context of what you're analysing I can't be more specific I'm afraid!