Due to our knowledge of the Shang being based almost entirely on secondary histories produced during the Han dynasty and substantiated by oracle bones and other archaeological evidence, I don't believe there is a "modern, generally accepted" time frame for the beginning of the Shang dynasty. Their predecessors, the Xia, are considered mythological, which makes selecting a definitive starting point very difficult, if not impossible. Writing in China began during the Shang dynasty, but the primary evidence of its use available to us is the aforementioned oracle bones. While providing insight to day-to-day concerns of the central state and the role of prophecy in decision making, it provides little in the way of chronologically sound record keeping.

The "Reception" section of the Wikipedia article for the X-S-Z Chronology Project goes into greater detail (with sources) regarding the concerns raised by the project's critics. Controversy aside, it is, as I understand it, the most recent large-scale project to determine the origins of the Shang, and its findings regarding the Shang does seem to be what is reflected elsewhere in literature.