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The Persian Monarchs were never worshipped as divine by the priests of Ahura-Mazda as they were strict monotheists.

Not quite correct. While they were not supremely divine as Ahura Mazda, and subordinate to him, they were spiritually clearly of (quasi)divine status. Shapur's inscription reads:

"Worshipper of Ahuramazda, the god Shapur, king of kings of the Aryans and non-Aryans, of divine descent, son of the Mazda worshiper, the god Ardashir (Artaxerxes), king of kings of the Aryans, grandson of the god-king Papak."

The king and his royal predecessors are subordinate to Ahura Mazda, but clearly divine.

The inscriptions for Shapur II and III say "from the divine race of God", although in this case it's debatable whether this could mean all Iranians, and not only the King.

Whether they were actually worshipped is another thing, but they saw themselves as godlike.

I didn't say that Augustus is Persian in origin, but Avestan, which is, as you correctly say, the common root. The "aojishta" was to the Zoroastrians the attribute of the Fravashi, the angel-spirits of great personalities (including the King). Maybe I should have contexted that point a bit more.

I think Alexander was influenced by the Oracle at Ammon-Zeus in Libya of his divinity than by any Persians.

This may be correct, the Egyptians (and the Greek oracle in Siwa obviously saw themselves as having authority to declare Alexander Pharaoh) gave their Pharaohs also divine status, however historical record shows clearly that Alexander tried to establish himself as legitimate heir of the Persian kings, adopting their role, marrying a princess, and taking over their traditions, dress etc. much to the chagrin of his Greek/Macedonian comrades... and this persianate hellenistic traditions were later emulated by the Romans. I.e. the "proskynesis" was again adopted by Diocletian.

Not to quibble, but most ancient people claimed divine descent. It is meaningless. I still stand by the claim that that no Persian monarch was worshipped as a God, certainly not in Alexander's time.

The Oracle at Siwah did not proclaim Alexander as Pharoah. That was a prerogative of the Egyptian priests of Amun Ra. They just confirmed that he was son of a Zeus. The Temple of Erythrae had also proclaimed his divinity at this time.

Later, one of his successors, Seleucus, proclaimed himself a son of Apollo. Of course, he was following Alexander's example, not any other.