1/16th actually isn't a risk for levels 1, 2, 3 and the first 33 seconds of level 4 because Kong doesn't actually throw the standard "1/16th type" until L5 difficulty kicks in.
Your problem on those boards is actually worse, because that's when he's still throwing pinballers and murder barrels. 1/16thing is simple in comparison.
You're still in massive danger under Kong, but it's not 1/16th danger. Grit your teeth, pray you get the hammer in time, then get to the L1, 2, 3, 4 safe spot under his leg.