OK, I'll take a stab at this -- Gurus, please correct me when I err!
First off, your complaint of having to slow down while towing a grade simply says that the truck isn't making enough HP & torque to maintain a given speed before EGT's climb to an unacceptable level, or that the engine can't breathe enough to keep temps down.
To make power, you have to burn fuel. You have a limited space in which to do this --the more fuel you pour in this space, the higher the EGT's will go. To reduce the EGT's, the engine has to breathe more freely -- there are several things that control this, including the size of your turbo housing, exhaust piping, engine timing, and of course, air flow in and air flow out.
Another way to increase the air flow is to spin your motor faster, which is why shifting down can result in a dramatic EGT drop: I've gone from 1200 to 700 in 20 seconds. You can also cool the combustion chamber with water injection -- I've heard propane also helps keep EGT's down, but in my book that stuff is more hassle than it's worth unless you are going for huge numbers.
So, leaving your engine's breathing apparatus the way it is and dumping more fuel in(larger injectors, turning up the pump) will result in more power(increased HP & torque), but also higher EGT's. The added torque & HP may or may not be enough to enable you to pull at the desired speed before EGT's rise too high. If you keep adding fuel, at some point the turbo you have will not be able to supply enough air to support the added fuel and you'll need a bigger turbo.
What I'm trying to say is that when increasing horsepower, you have to balance the air in/out with the fuel you are asking the engine to burn to keep EGT's in a manageable range. If you make a change that adds fuel, watch your EGT's and see if they go up -- if so, then you need to do something to help the engine breathe better.
I don't know what a Banks stinger kit consists of, so I can't comment on that. A 6 speed just adds another gear so you split the gears a little more frequently -- I don't think that would be a significant change in at-speed towing. My approach would be to add a little fuel, see what happens and make modifications based on what the engine says it needs.
Sorry for the long winded post!