Before every one piles on, go back and look at the OP's question.
Basically what I am wondering is can you get the same velocities as a longer barrel out of a shorter barrel by using a faster burning powder? For .308 Win, out of a 24" barrel, a 180 grain bullet will move at 2550 fps. Let say (for the sake of not knowing what actual powder was used) 49 grains of H414 was used to get this velocity. If you were to cut that barrel down to 16" you would get a velocity of 2370 fps with the same 180 grain bullet. If you were to use a faster burning powder like H4895 in the 16" barrel, would you be able to bring the velocity back up to 2550 fps? If so, would this be dangerous, pressure wise?
My answer to this question is, ....
POSSIBLY...
Look at it in general terms, don't get wrapped up in the details of how much of what powder, etc.
Just for example, lets say your bullet is moving at 2500fps out of a 24" barrel, and you want to duplicate that from a 16" barrel. Can you do that? Possibly. Will it be safe?? POSSIBLY.
However, its unlikely to be able to be done with existing equipment, and simply cannot BE done with identical pressures.
Look at it this way, you want to match speed with an acceleration path only 2/3 as long. (16 vs 24"). The only way to do that is to accelerate the bullet faster in the shorter tube. Doing that requires more force (pressure), in order to compensate for the shorter duration of the acceleration.
"Faster" burning powders MAY be able to do this, depending on specifics of the situation and the factors involved, but there is a limit to that ability, and that may fall well short of your desired goal, which is matching the speed at safe working pressure.
One analogy I like is the safe door. Consider that the bullet. Now, SLAP the safe door. IT moves very little. PUSH that same door, and it moves, and keeps moving as its pushed. That is "fast vs. slow" burning powder's effect.
This is an illustration of principle. Nothing else.
There are so many factors involved getting 24" barrel speed from a 16" barrel that a simple yes or no answer isn't going to be correct, depending on all those other factors.
Just to keep it in round numbers easy to comprehend, consider, if it takes X pressure to accelerate the bullet to speed in a 24" then to get that same speed from a barrel only 2/3 as long, you would need to increase the pressure by 1/3, according to straight linear math.
But gunpowder pressure isn't always a straight linear thing. SO, I say
possibly you can do it. But its no where near as simple as just using a faster burning powder.