Interesting conundrum, with persuasive arguments on both sides. I can add a few observations.
First, the two Austrian tax marks, to my mind, are of little help in judging authenticity. If both the marks and piece are genuine, their appearance arouses no suspicions, as they would very properly appear on a baroque piece which survived through the Napoleonic Wars in Austria. If the piece is authentic but the marks are not, it could be explained that, as noted, these marks might well have been falsified to avoid the tax on (and later confiscation of) the piece during the era the legitimate marks were used. If neither the marks nor the piece are genuine, then there, too, the marks may have been added for verisimilitude, as indeed we know at least one was in Hanau. (Karl Knies' book
Die Punzierung in Oesterreich describing and illustrating these marks was published in 1896, so their form and function was known to Hanau makers - and outright forgers - at the time.) So these really are a moot point to my mind, since they can be explained in every scenario.
Second, if genuine, the maker's mark is that of Jakob Beckhausen, master 1678, died 1705. (See maker/mark G472 A in the same reference I cite in this recent thread:
Old Spoon from Gdansk). That would make the box last quarter 17th century (or the very first years of the 18th). Stylistically, the box is certainly consistent with this.
Third, while the galants scene very much looks like Hanau historizmus, I do notice that the man's costume is remarkably accurate. Oddly enough, men's costume is much more easily (and narrowly) dated from about 1650 to 1790 than women's, changing more rapidly and with much less subtlety. The hair, the coat, the hose and (especially) the square-toed shoes with "cupid's bow" tongue are all spot-on correct for the last quarter of the 17th century. This meticulous attention to period detail is not a feature I associate with Hanau makers.
On balance, I lean towards the box being authentic late 17th century Gdansk, but I would not say more without being able to examine the piece in person. Thanks for the interesting and intriguing post!