For those who may find this thread at a later date, from the Core Rules
FAQ:
Add the following paragraphs to the end of this Rare Rules entry:
Note that it doesn’t matter how many rules are affecting a unit that enable it to fight first, or how many rules are affecting it that say it cannot be selected to fight until after all other units have done so – if a unit is under the effects of one or more of both kinds of ability simultaneously, that unit instead fights as if none of those rules are affecting it.