The check in the Improved Natural Attack feat is coded to required certain combinations of component.? tags that an Unarmed Strike can't meet.
But you can use an adjustment to change the candidate string for the feat's selections.
(I tested this at Final:5000, but it just needs to be after the HasAbility.? tag would have been added.)
Code:
doneif (field[pIsOn].value <> 1)
doneif (hero.tagis[HasAbility.cMnkUnarm] = 0)
foreach pick in Hero where "thingid.fImpNatAtt"
eachpick.field[usrCandid1].text &= " | (component.BaseWep & wFtrGroup.Natural)"
nexteach
(And FYI, there was official errata for the Bestiary which specifically disallowed Unarmed Strike as an option for that feat, so it's just a house rule for you to allow it and not a loophole anymore.)