All else being equal, the case having the highest capacity can run at a given velocity at a lower pressure compared to a lesser capacity case.
simply need more powder in the thinner case to get to those velocities
Yes, very true, you will have to run a bit more powder to do it. Ultimately though, higher velocities can be achieved. That is how a .300 WinMag runs 3200 fps with a 165 grain bullet vs the .30-06 at 2850 or 2900 fps--more volume of gas. It's kinda oversimplifying, given burn rates are not being considered, but....
Same is true of a .45-90 vs .45-70. Run a 500 grain bullet at 1500 fps. Which case has the lower pressure(disregard charge needed, this is another subject)? OK, now run both at 40 Kpsi. Which one has the highest velocity? .45-90 in both cases(no pun intended).
Yes Pumkinchunker, you can run your .44 load in your .444 brass, but if you want the velocity to be the same as in the .44 brass, you will have to increase the charge. The gas simply has more room to expand into, and if you want to do as much work, you have to provide more gas. The larger volume will also push for a longer period of time, providing the additional velocity. You will, in addition, be able to utilize slower burning powders even more to your advantage.
The downside is recoil. Weight of the charge is part of the ejecta. Ejecta makes kick...Your 45-90 will kick a little harder at the same velocity as a .45-70, whether you can detect it or not, but the calculations bear it out.
You also have the right idea in placing the bullet closer to the rifling.