Good news for those interested in Shāh Jahān's reign (r. 1628-58), as two new projects from the Institut für Iranistik at the Österreichischen Akademie der Wissenschaften, seek to examine at greater depth the historiographic and architectural production during the time period. The first of the two projects will, in addition to producing an analytic study of history writing under Shāh Jahān, undertake a translation of Qazvīnī's Bādshāhnāma (though unclear whether to German or English, I'm naturally rooting for the latter).
For an introductory survey of sources for Shāh Jahān's reign see M. Hidayat Hosain, "Contemporary Historians During the Reign of the Emperor Shāh Jahān," Islamic Culture 15 no. 1 (1941): 64-78.