I have to admit, I'm not entirely sure what you mean by "a total reconstruction of the Persian Empire." Obviously, neither Ardashir I nor his successor managed to recreate the political influence or reach of the Achaemenid Persian Empire in the 6th-4th Centuries BCE. In fact, it is not at all clear how much of the Achaemenid dynasty's history was actually remembered in Persia by Ardashir's time - the 3rd Century CE. The popular claim that Ardashir announced to the Roman's that he sought to rebuild the Achaemenid borders traces back to Roman historians. No Persian sources substantiate that claim.

Admittedly, there are fewer surviving Persian sources, which tend to be less detailed. However, the Letter of Tansar, purports to be a kind of statement of purpose for Ardashir I penned by his high priest, the eponymous Tansar. In actuality, the letter shows a degree of ignorance regarding Alexander the Great's conquest of Persia and little familiarity with anything before that at all. The version of the letter that has been preserved is most likely a 5th-6th Century copy of the 3rd Century original edited for propoganda purposes in the later Sassanid period. However, linguistic evidence still suggests that most of the letter is original material, and it's hard to imagine why evidence for greater imperial ambition and Persian history would have been redacted.

This is in line with most of the surviving Sassanid literature. It's all from the latter half of Sassanid history, and most of it shows near-total ignorance of the original Persian empire and its kings. That period was largely refilled by the mythical Kayanian kings, a group of legendary Zoroastrian heroes. Even the Hellenistic and Parthian periods were largely obscured in later Sassanid and medieval Iranian literature, compressing half a millennium of non-Persian rule down to about 200 years in their own historical narrative.

Ardashir I's political program was much closer to your second option, though it was not a "new boss, same as the old boss," situation. Most of the Parthian empires institutions, administrative units, and pro-Ardashir noble families remained intact. Cadet branches of the Parthian Arsacid royal family even retained power in several client kingdoms. The primary exception to this general trend was simply that more of the royal administration was moved from the old Arsacid power centers in the north like Ecbatana and Hekatompylos to new Persian strongholds like Estakhr and Gor.

While the existing Parthian system remained intact, Ardashir did initiate a process of gradual change. The Parthians had relied on a network of local kings in and around their empire to act as clients or vassals. Powerful noble families had significant autonomy within their own territory even if they didn't officially hold the title of king (shah). When Ardashir defeated pro-Parthian loyalists, he did not simply put his own men into the existing hierarchy. Instead, he embarked on a campaign of centralization. Instead of local hereditary dynasties, administration in the Sassanid Empire gradually transitioned to centrally appointed political offices.

This was not a revival of the old Achaemenid satrapy system. Instead, Ardashir and his successors wove a complex web of military commanders and pseudo-feudal political offices. Some of these offices were allowed to pass from father to son, but that was not a given. The appointment had to be reconfirmed by the king, who could reassign these new local governors at will. This process was initiated by Ardashir I, but progressed slowly as opportunities to centralize power presented themselves over generations of Sassanid kings.

This political centralization was accompanied by an addition to the Parthian state apparatus. The Arsacid dynasty didn't interfere much in religious matters. The Jewish diaspora, Christianity, and Buddhism were generally comfortable spreading under the Parthians. Local variations of Zoroastrianism operated largely unhindered as did pagan Mesopotamian and Greek beliefs.

Ardashir didn't initiate a campaign to proselytize and convert these various minority groups to Zoroastrianism, but he and Tansar did incorporate religion into their centralization efforts. At the intersection of political and religious reforms, Ardashir instituted new limits on minority communities. Under the Parthians, minority religions, most notably Jews, were allowed to follow their own laws governed by their own courts. Ardashir brought them under the same legal jurisdiction as the rest of the empire.

In a more explicitly religious context, Ardashir always presented himself as Zoroastrian ruler, first and foremost. He had the favor of Ahura Mazda and the Letter of Tansar described religious fervor as one of Ardashir's primary motivations for taking over the empire. As a piece of religious propaganda, that aspect of the letter is dubious, but the importance of religion under Ardashir is still evident.

Ardashir initiated another slow process of consolidation within Zoroastrianism. There had never been an empire-wide Zoroastrian institution before. Local communities had slightly variations on practice and interpretation. Local priests were more or less autonomous. Ardashir was the first king to try and define Zoroastrian orthodoxy in law and force all Zoroastrian communities to abide by that orthodoxy.

Once again, this shift was not immediate. For example, Ardashir's son, Shapur I, did not demonstrate the same religious fervor and allowed Manichaeism to develop during his reign. However, Ardashir's religious reforms were enough to concentrate significant economic and political influence in the hands of the Zoroastrian priesthood. In the reign of Ardashir's grandson, Bahram I, that influence had grown enough that the priesthood was able to influence Bahram and his successor to actively persecute religious minorities.