Really cool (old) thread, guys. I have a Bohemond lll example, just considered it a cool crusader coin, but I learned a bunch here.
This one showed up a few days ago, while real life was intervening. The dealer attributed it to Bohemond (IV-) V. It corresponds to Malloy 126 ("Late Type /New Style"), citing Metcalf Class O, which attribute it less ambiguously to Bohemond V (1233-1252), while noting that, along with the stylistic variations, "[t]his type generally weighs less than the earlier coins of this design." This example's weight and module (even with likely clipping) correspond more to the earlier examples, inviting speculation that, in some sense, it's a transitional subissue.