Why do you think it is coil #4? It was replaced Dec 2013 and has about 16K miles on it
when it was replaced, was it replaced with a new OEM motorcraft coil?
was the spark plug as replaced at the same time?
if so, did you gap the spark plug or just throw it in assuming all was good?
was only the #4 coil replaced?
please do yourself a favor... instead of still trying to figure it out a day later, spend an hour and do a little searching as recommended and you will see a few hundred other threads that started just like this one. they all have the same outcome for a reason. the coils in the LS are prone to taking a sh!t, when said sh!t is taken, they have a side effect of emitting RF interference, this interference then is mistakenly identified as a problem with the throttle body. the #4 coil is in the closest position for the interference to be picked up (however #3 also has a high probability, and i would bet if the interference is strong enough any coil could do it...)
99% of the time when a coil fails it barely fails,meaning most of the time, its working fine. but ever once in a while it will miss fire, this is know as a marginal coil. also 99% of the time the cars computer wont detect the misfire and throw a code for it.
the bottom line is you must replace all of your coils (as once one starts to fail, more are on their way out. also it cost less to replace them all then it does to test them to find out which one is bad) and plugs. more than likely this will completely cure the problem, but in the slight case that you have further problem, you need to be 100% sure that they are not contributing to the issue. also when you buy cheap ass coils, they usually fail much faster and that if they all show up being good.