There are several problems with this sort of mass conversion to Judaism. Judaism is not missionary, never really has been but lets wave that one away. One of the "issues" that Christianity dealt with early on was the issue of Jewish law - circumcision, kosher food rules, and much more (613 mitzvot). The appearance of Christ and his dispensation of sin did away with that, making conversion much easier and Christianity is aggressively missionary. Islam does have some "rules" such as halal food (not as restrictive as kosher), no alcohol, and circumcision but less than Judaism. Islam was also aggressively missionary, spread by the sword especially against pagans more so than Christianity, and had formalized disabilities for non-Muslims especially pagans. Perhaps most importantly, Judaism was never the religion of the winners - either top down as in the later Roman Empire and gradually in Europe or the religion of the conquering armies.
For the average Joe or Jane in the ancient or early medieval world, most of the time the motivation for accepting a new religion was going along to get along. Sure there were cases of spiritual conversion, but for most this was not the case. When the new overlords made it clear it was in your best interest to convert, this tended to happen (no matter what religion you had before). Some conquerors, such as the Mongols, really didn't care what religion their subjects had, so you did not see mass conversion with Mongol conquest. Others, both Christian and Muslim, made acceptance of their religion a real plus for the newly conquered people.
IMHO to make one of these mass conversions to Judaism, and not just of an elite (like Khazaria), you need to make Judaism aggressively missionary, and seen as the religion of the winners.