I agree with you, Richard, that it would be clearer to put “only” immediately before the word or phrase it modifies, but that is not the point here. When Michael Swan says “when 'only' refers to another part of a sentence, it often goes in 'mid-position' with the verb”, he is describing how English is usually spoken by educated (and “uneducated”) native speakers. His description is absolutely correct — that is how real native speakers really speak. That is why is “sounds good” to native speakers, and that is why ESL learners want to learn “natural” English as opposed to so-called “textbook” English. (Actually, a good textbook will present natural English as well.) So, we can either describe English as it is really used by educated native speakers, or we can tell them how they are “supposed to” speak — in somebody's opinion. While I certainly do help students to develop clear communication skills, the emphasis is on how educated native speakers communicate in the real world — not in an ideal world. Otherwise, there’s always Esperanto….

I'll use an arrow to show the choices I think are the most natural. If they both seem equally, I'll put arrows in front of both. Oddly, in the first two examples, your wording seems clearer and more specific, but, nevertheless, I like the sound of the first one better.

--> She only reads biographies. [But this could also mean she doesn't sing them or write them].

She reads only biographies.

-->I only like swimming in the sea. [But this could also mean you don't like diving or wading in the sea].

I like swimming only in the sea.

She is only on duty on Tuesdays.

-->She is on duty only on Tuesdays.

-->She was only talking like that because she was nervous. [Both mean the same thing.]

-->She was talking like that only because she was nervous. 

-->I've only been to India once. [But I've been to Pakistan many times.]

-->I've been to India only once. [But I'd like to go there again.]

Off-topic, but I remember an illustration of a sentence that, it was claimed, had many different meaning depending on where you put the word "only:"

Only I hit him in his eye yesterday. [Nobody else did.]

I only hit him in his eye yesterday. [I didn't do anything worse.]

I hit only him in his eye yesterday. [He was the only person I hit in the eye.]

I hit him only in his eye yesterday. [The eye was the only place I hit him.]

I hit him in only his eye yesterday. [The eye was the only place I hit him.]

I hit him in his only eye yesterday. [He only has one eye and I hit him in it.]

I hit him in his eye only yesterday. [It wasn't a long time ago, it was just yesterday].

I hit him in his eye yesterday only. [I didn't hit him today, or the day before yesterday, or any other day].

Richard,

the sentences in blue sound more natural to my ear, but I can easily explain it: this word order is common for Russian.

Dan Smith,

Don't be so aggressive! Don't ever hit him in any part of his body! :)

Isn’t sometimes the meaning different?

I only like swimming in the sea. 

-> The only sports I like is swimming in the sea. (I don’t like other sports like cycling, horse riding, skiing.)

-> When it comes to swimming, I only like to do it in the sea. (I don’t like swimming in pools.)

At least that’s how I as a non-native understand the sentences. I found this explanation: https://dictionary.cambridge.org/de/grammatik/britisch-grammatik/only

I don't like any in blue, others sound more natural to me. If they taught us grammar in school here in the US I was sleeping through it.