It's not that complicated. The god concept that is coherent is the one you refer to when you say, "To reject all gods..." meaningfully in a sentence.
By "all gods" in that sentence, I mean "all individual members in the set 'gods'", not "all individuals that meet the objective criteria for godhood." I make no claim about there being any common characteristics shared by all members of the set "gods" other than the fact they have been put into that set.
Edit: maybe an analogy will help illustrate what I'm getting at: say that we're trying to establish that there are no living Norwegian tennis grand masters (just to pull a category out of the air - for argument's sake, let's say it's true). We can define the list: we can look up the seeding lists and find out all the Norwegians who ever achieved grand master status. But how would we go about affirming that they're all dead... i.e. rejecting that they're all alive?
If things were different, we might be able to reject them as a category: if the country of Norway had ceased to exist 1000 years ago, or if tennis hadn't been invented yet, then we could safely conclude that no living Norwegian had ever played it. However, we can't do this. Instead, we'd have to go through the list one by one and go "person 1 is dead? Check. Person 2 is dead? Check." ... And so on until we get through the whole list.
... but since none of the criteria for getting onto the list "Norwegian tennis grand masters" speak to whether a person on the list is alive or not, the mere fact that a person is on the list isn't enough for us to know whether or not he or she is dead.
Does that make my point clearer?