Which of the seven fold reasons does this fall under?

It's probably useful to take a few steps back first, since this text is from Chandrakirti, an author which views differ significantly from some of the core principles of other schools in his branch of Buddhism.

The linked text originates in the Madhyamaka school of Nagarjuna, which means that as a basic principle, author will view all phenomena as ultimately empty of intrinsic nature or self-existence (svabhāva). Furthermore, all things (bhāva) have two natures, the conventional and the ultimate

As such, the conventional truth (saṁvṛti satya) implies that, as a matter of human convention, phenomena have a nature or existence (bhāva), for example ice has the property of being cold. The world-view of conventional truth is the building block of human communication that allows us to build societies.

As for ultimate truth, well, this is where Madhyamaka branches off in different schools of thought, like Sautrāntika, Kamalaśīla, Yogācāra and Prāsaṅgika (Chandrakirti belongs to the latter). It would take way too long to detail the differences here. If you're interested, The Theory of Two Truths in India is an excellent read.

In essence, Candrakīrti rejects the theories of the two truths in both Brahmanical and the Buddhist schools of Vaibhāṣika, Sautrāntika, Yogācāra and Svātantrika Madhyamaka. At the core of the Prāsaṅgika's theory of the two truths are these two fundamental theses:

• Only what is conventionally non-intrinsic is causally effective, for only those phenomena, the conventional nature of which is non-intrinsically real, are subject to conditioned or dependent arising. Conventional reality (or dependently arisen phenomenon), given it is causally effective, is therefore always intrinsically unreal. Hence that which is conventionally (or dependently) coarisen is always conventionally (or dependently) arisen.

• Only what is ultimately non-intrinsic is causally effective, for only those phenomena, the ultimate nature of which is non-intrinsically real, are subject to conditioned arising. Ultimate truth (or emptiness), given it is causally effective, is therefore intrinsically unreal. Hence ultimate truth is ultimately unreal (or emptiness is always empty)

Madhyamaka schools generally state that all phenomena are merely conceptual constructs (prajñaptimatra) which do not exist in themselves but are mentally constructed dependent designations (prajñāptirupādāya). However, Chandraktiri views even conventional truth (which is not a phenomenon, but a mental state or construct) as empty of intrinsic natures. As such, he defines ultimate truth as:

"the nature of things found by particular exalted cognitive processes (yeshes) of those who perceive reality."

Now with this in consideration, let's take a look at your statement:

The conventional self is not different to all its parts (is composed only of parts) but not the same as any part (does not depend on any part)...this arguably, is a reason to think that the self cannot be destroyed

Candrakīrti attributes three senses to the term convention:

• confusion (avidyā) for it obstructs the mundane cognitive processes of the ordinary beings from seeing the reality as it is by way of concealing (saṃvṛti) its nature;

• codependent (paraparasaṃbhavana) for it is an interdependent phenomenon

• Signifier (saṁket) or worldly convention (lokavyavahāra) in the sense of dependently designated by means of expression and expressed, consciousness and object of consciousness

All 3 senses can be applied to your statement, giving very different renditions pointing to the same underlying conventional truth. For example:

• the conventional self, like all phenomena, is subject to constant change. Its acclaimed parts are therefore also subject to change. Since there is no "constant" conventional self, there is no "constant" that cannot be destroyed.

• if the conventional self arises dependent on its parts, then essentially there is no intrinsic self that cannot be destroyed.

• as a worldly convention, we interact with our and other "selves" as mental constructs for convenience of communication. Nothing in this convention however points to these "selves" being indestructible.

Remember that all these constructs are built upon conventional reality, which Chandraktiri views as empty of intrinsic natures.

Identification with consciousness of an infinity of parts and non-parts is incomplete:

MN1:16.1: They perceive the dimension of infinite consciousness as the dimension of infinite consciousness.
MN1:16.2: But then they identify with the dimension of infinite consciousness …
MN1:16.3: Why is that?
MN1:16.4: Because they haven’t completely understood it, I say.

Also consult DN1, which describes 62 grounds for getting caught up in theories of self and cosmos.

DN1:3.70.1: Now, when those ascetics and brahmins theorize about the past and the future on these sixty-two grounds, it is not possible that they should experience these things without contact.
...
DN1:3.72.2: All of these ascetics and brahmins who theorize about the past or the future are trapped in the net of these sixty-two grounds, so that wherever they emerge they are caught and trapped in this very net.

Rather than look at all the parts or not-parts, perhaps we should best examine the first four words of the seven reasons.

The self is not ...

Without self, what reason would there be to look for parts or not parts?