pmda, your question, cur “quem?”, really goes much deeper than you may have thought.
The problem is that baculum/s is an object that rarely if ever acts as an agent and therefore rarely appears in the nominative. (I suspect that this may be why the neuter nominative singular 2d declension ending in both Latin and Greek is identical to the masculine accusative, and why in both language, as well as in Russian, neuter nominative and accusative endings are always identical. There must be something pre-proto-Indo-European in this.)
Both of the instances in Ovid cited as doubtful evidence for baculus look like errors in the manuscript tradition, and the modern editors (the Teubner Fasti of Alton, Wormell and Courtney, and Tarrant’s Oxford Metamorphoses) treat the word as neuter.
At Fasti 1.177, the oldest manuscript, which dates from the 10th century and is now preserved in the Vatican Libarary, reads incumbens baculo quod [actually, qd] dextra gerebat (“leaning on a staff, which his right hand held”), against the other manuscripts’ baculo quem. The Teubner editors read quod.
Metamorphoses 2.789: baculumque capit quod spinea totum/ uincula cingebant (“and she grabbed a wand which was entirely girded with chains of thorns”–this is Invidia, the personification of Envy). Most of the manuscripts read quem, but again, a 10th century German manuscript in the British Museum reads quod, and an 11th century Italian manuscript now in Florence appears to have read quod before being “corrected” to quem.
Metamorphoses 2.681 is just about conclusive evidence that Ovid treated baculum as neuter. Here, the word does appear in the nominative, and, again, most of the manuscripts, with the exception of the same 11th century Italian manuscript in Florence prior to “correction,” read baculus. However, the word is modified by the neuter adjective siluestre, which is guaranteed by the meter, so Ovid must have written baculum. And baculum . . . agreste appears again (in the accusative), with a metrical guarantee, at 15.655.
So it looks like Ovid treated the word as neuter, but it was liable to be mistakenly changed subsequently to masculine in the Ovidian manuscript tradition by scribes who thought it was masculine, after the word itself underwent a change in gender in post-Ovidian times.
(continued)