Well, it's a bit difficult.
First of all, the Parni largely survived because Seleucus II campaigned in the East to reestablish Seleucid control; this prompted Diodotus, the satrap of Bactria, to switch sides, because he thought that the Parthians could be a useful buffer between him and the Seleucids (this cost him his life, but that's a different story). If Andragoras had managed to fend off the nomadic Parni and keep control of his satrapy, he would still likely be defeated by Seleucus II; and even if he managed to defeat and kill Seleucus, he would have to face Diodotus, who would likely try to expand his influence in Parthia and could actually achieve that with little trouble and the support of the legitimate government in Antioch. Andragoras would be in a weaker position, isolated and facing the most powerful satrap east of the Zagros mountains: the most likely result would perhaps be a sort of large, Bactria-centered eastern viceroyalty, depending on what concessions Diodotus could get from Antioch.
If you want a Hellenistic state under strong Greek influence, a better pod in my view would be the rebellion of Molon:
Molon was the governor of Media. In the chaos that followed the murderof Seleucus III during his campaign against Attalus I of Pergamum, he declared his independence in Media and with the support of his brother Alexander, the governor of Persis and Artabarzanes, the king of Media Atropatene, he invaded Mesopotamia, reaching as far as Ctesiphon and after his victory over the royal army sent against him in 221 B.C., he controlled most of Mesopotamia and the remaining Upper Satrapies. Ultimately, however, he was defeated and killed by Antiochus III.
But another obscure point of that period is that, in the summer of 221 B.C., Antiochus invaded Coele Syria but was repelled by Theodorus, a general of the Ptolemaic army. Now, during this invasion, he had reached in the valley between the Lebanon and Antilebanon mountains. Suppose that Theodorus manages to get the local tribes to join him. The tribesmen organise an ambush , during which they manage to inflict heavy losses to the Seleucid army; among the dead is the young king Antiochus. This development creates a crisis in Antioch. The old king Ptolemy III may decide that it would be a good idea to intervene in Syria, in order to prevent it from falling into the hands of Achaeus, the late king's uncle and a fairly competent general. He also comes in contact with Molon, whom he offers recognition for his eastern kingdom in exchange for Molon promising to intervene west of the Euphrates. Thus the Ptolemaic army enters Syria and secures the area. Achaeus may have wanted to claim the Seleucid crown for himself, but he doesn't move, largely because he has to keep an eye on Attalus, but also because he would be unable at that stage to win alone against Egypt. Perhaps, to make this partition more certain, we could have Achaeus actually move try to move in Syria, which in turn could embolden Attalus to invade the Seleucid territories of Asia Minor again, forcing Achaeus to turn back, only to be defeated and killed during the batte; the subsequent division of the Seleucid realm between Egypt, which would control Syria and Cilicia, Attalus, who would be content with maintaining the new status quo and Molon, who would also be content with his gains and would likely be more interested in the east. Thus you could get this way a hellenistic state east of the Euphrates covering most of the lands of the OTL Parthian empire, ruled by a Greek dynasty and heavily influenced by Greek culture.
I don't know if this is would fit what you have asked for or if my ideas are all that good, but I think that is a fairly goodand realistic way to get what I described in the last sentence. Feel free to correct me if I am wrong anywhere

