The monumental/architectural sculptures of Petra - has there been any research on the likely craftsmen who executed them?

The Nabateans had given up the nomadic life long before the construction of the most famous buildings at Petra, such as the Treasury in the 1st century AD. Petra had been the Nabatean capital for around 400 years at this point, and the Nabateans had been Hellenized since 150 BC--they were even ruled by kings with names like Aretas III Philhellene. By the time the most distinctive buildings in Petra were constructed, the Nabateans were a powerful, Hellenized kingdom caught up in a geopolitical struggle with Herod Antipas and the Emperor Tiberius.

There is archaeological evidence for several centuries of Nabatean architecture before the famous buildings of Petra. For example, Avdat was founded by the Nabateans in the 3rd century BC, and there is evidence of a large acropolis there. Mamshit (1st century BC) is a small city, but particularly well-preserved and has evidence of luxurious architecture. Another site with "characteristic Nabatean rock-cut architecture" can be found in Mada'in Saleh. The UNESCO report on this site notes the presence of 111 monumental tombs. The presence of Nabatean craftsmen is implied by the inscriptions in the Nabatean language on 30 of these monuments. The report further states that:

the site was worked on by the Nabataeans from the 1st century BCE and probably from even earlier.

The UNESCO report mentions two other archaeological sites deeper in Saudi Arabia that display the typically Nabatean rock-cut architecture. Basically, there is plenty of archaeological evidence that the Nabateans had the resources and craftsmanship to construct cities like Petra while relying largely on their own resources.

Despite the wealth and importance of the Nabateans, we apparently don't know much about their society. Much of what we know about older Nabatean culture comes from Strabo. This little knowledge suggests that the Nabateans did much of their construction on their own:

We still know comparatively little about Nabatean society. However, we do know that they spoke a dialect of Arabic and later on adopted Aramaic. Much of what is now known about Nabatean culture comes from the writings of the Roman scholar Strabo. He recorded that their community was governed by a royal family, although a strong spirit of democracy prevailed. According to him there were no slaves in Nabatean society, and all members shared in work duties. The Nabateans worshipped a pantheon of deities, chief among which were the sun god Dushara and the goddess Allat. (source)

Update: @TylerDurden suggested the Smithsonian as a source. This article seems to support native Nabatean craftsmanship. For example:

By the second century B.C., Nabateans dominated the incense trade from southern Arabia. Within several decades, they had assembled a mercantile empire stretching for hundreds of miles. The people who a few generations earlier had been nomads were now producing eggshell-thin pottery, among the finest in the ancient world, as well as grand architecture. . . .

Accustomed to tents, the early Nabateans had no significant building traditions, so with their sudden disposable income they drew on styles ranging from Greek to Egyptian to Mesopotamian to Indian—hence the columns at the Great Temple topped with Asian elephant heads. "They borrowed from everybody" . . .

One of Petra's mysteries is why the Nabateans plowed so much of their wealth into carving their remarkable facades and caves, which lasted long after the city's free-standing buildings collapsed from earthquakes and neglect. The soft stone cliffs made it possible to hollow out caves and sculpt elaborate porticoes, which the Nabateans painted, presumably in garish colors . . .

At its peak, Petra's population was about 30,000, an astonishing density made possible in the arid climate by clever engineering. Petrans carved channels through solid rock, gathering winter rains into hundreds of vast cisterns for use in the dry summers.