In this answer, I learned that with "correct" French, you aren't supposed to use possessive determiners for body parts ("ma tête, mes jambes"), but instead use a definite article ("la tête, les jambes").
The reply you quote didn't clearly stated this "rule1" only apply to sentence like:
Elle aime masser ses jambes.
The reason is primarily to avoid ambiguity as ses jambes doesn't tell whose legs they are. That means the sentence is grammatically correct but its style would be improved/clarified by using a reflexive construction.
Using possessive determiners for body parts is certainly possible and correct in many cases.
What is generally considered incorrect is using a redundant determiner like in:
Elle aime se masser ses jambes.
A similar redundancy is:
J'ai mal à ma tête.
but it is less criticized. Redundancy is not forbidden in French. It can be used to emphasize something. It might also be used when talking to kids to make clearer what is said. Reciprocally, redundancy is what naturally comes to kids lips when talking.
The reason is only your own head can aches, not someone else's head so we use:
J'ai mal à la tête.
About the forms you quoted, je m'installe sur le dos is the only possible way to tell it. The bogus j'installe sur mon dos would be missing a direct object: "I install on my back" (I install what?)
Je replie mes jambes is less easy to sort out. Je me replie les jambes would be grammatically irreprochable but doesn't happen to be idiomatic. That's not the case with je me bouche les oreilles which is equivalent to je bouche mes oreilles.
Je m'installe sur le dos is the only possible way to tell it. The bogus j'installe sur mon dos would be missing a direct object: "I install on my back" (I install what?)
Je replie mes jambes is less easy to sort out. Je me replie les jambes would be grammatically irreprochable but doesn't happen to be idiomatic. That's not the case with je me bouche les oreilles which is equivalent to je bouche mes oreilles.
Avec mes deux mains and avec les deux mains are both idiomatic and in my opinion could have been used interchangeably.
On the other hand 😉 avec mes dix doigts sounds better than avec les dix doigts. The last form might trigger the question: "which ones?"
1 I wouldn't call it a rule but a mild recommendation