Are the vortex generators on the Cessna Caravan necessary and sufficient for safety of flight?
You need to keep several things apart:


The center of pressure is where all vertical aerodynamic forces can be summed up. It does not have a fixed location, but its location changes with angle of attack.
The aerodynamic center (or neutral point) is indeed at about 25% of the chord of a wing. Its location is fixed as long as the wing planform does not change.
The neutral point of the whole airplane is the weighted mean of the local neutral points of all horizontal surfaces. This is the most important neutral point for longitudinal stability.


In flight you will shift the center of pressure such that it is at the same longitudinal station as the center of gravity. You do this by regulating the tail lift or downforce with the help of the elevator.


  When center of pressure, $\text{c}_p$, is forward of the center of gravity, $\text{c}_g$, then [this] necessitates an up-force on the horizontal tail in order to maintain level flight.


This is true if you speak of the wing's center of pressure. In a conventional configuration like the Cessna 208 the wing's center of pressure is ahead of the airplane's center of pressure.


  How typical is it that aft-$\text{c}_g$ limits are behind the $\text{c}_p$, such as in the 208?


This is quite normal. No need for concern as long as the center of gravity is still ahead of the airplane's neutral point.


  Wouldn't this imply longitudinal static instability?


No. Stability is reduced compared to a more forward center of gravity location, but still positive.


  How do engineers typically design tails to maintain necessary up-forces in such cases?


The biggest concern of engineers in such a case are too light control forces. The force feedback loop is important for avoiding control deflections which could overstress the structure. Since the tail is in the downwash of the wing and carries less load per area than the wing, it is very, very unlikely that it stalls first. Without knowing the details, I am quite sure that the vortex generators were not added to cure a deficiency which occurs with a rear center of gravity location. Now I did some background reading and think that the vortex generators are needed to avoid early separation on the elevator in case of low-speed flight with flaps retracted and a rear center of gravity.


  Are vortex generators […] after-thought band-aids to remedy an inadequately designed tail?


Yes, they are. They normally cure one corner of the envelope where something went out of whack during flight testing or after a modification (say, an increase in gross weight or in the permissible center of gravity range).


  Does anyone have more published references about the Caravan's tail specifically?


Sorry, not me.



Now I have read the accident report and the linked transcript about the Caravan crash on October 10 in Dillingham, AK, in 2001. These are my remarks:


The witness in the transcript is very knowledgeable and I agree with all what he said.
His statement about the tail load change upon flap retraction seems spot on: Even though the accident report is inconclusive about the flap position, it seems likely that retracting the flaps coupled with insufficient lift on the tail made the aircraft pitch up and stall.
All the accident report has to say about de-icing focuses on the wing, but since lift-off speed seemed normal, I don't think ice on the wings was a problem. But what about ice on the tail? There is no mention of that.
Vortex generators on the upper side of the tail are unusual and a "red herring" about late fixes for insufficient pitch down control authority. Add some ice on the upper surface of the tail, and the fix will not be sufficient and cause an uncontrollable pitch-up with a rear center of gravity location.
That the pilot seemed to have pulled on the yoke on the way down did not help, either. Lift loss on the wing would cause a nose-down pitch change, but the aircraft remained stalled throughout its descent. Yes, it needs some effort to pitch down when the flight path is already 40° down, but this is the only way to avoid a crash. Remember AF447.


My conclusion from all this is that the Cessna 208 Caravan is stable and safe to fly as long as the tail is in pristine condition. Any contamination of ice and even de-icing fluid will compromise its ability to produce the required lift in low-speed flight with flaps retracted and a rear center of gravity.