In the email you sent to techsupport, you also mentioned that the noise was about plus or minus 5 feet. I am not sure it is possible to get both the accuracy and response time you are looking for. You could do more averaging to smooth out the reading more, but this will increase the delay before a change in height is detected. For the plane flight in this blog, the averaging was done over several seconds since response time was not an issue. You might have a better chance of using the LPS25H pressure sensor as it is generally less noisy so using it might help, but I would not expect it to be that much better. This blog post about the LPS25H might be useful when comparing the LPS331AP sensor to the LPS25H sensor.
In general, we usually recommend using a motor driver that has a continuous current rating greater than the stall current of your motor. From the motor specifications I found on this website, it seems like you should be able run two of those motors from each channel on the VNH5019.
I tested our Spring RC and Parallax continuous rotation servos over an update frequency range of 50Hz to 200Hz to see how they were affected. The only change in performance I noticed was that at slow speeds the servo moved a little bit faster with higher frequencies. However, the change was not a significant jump in performance, and changing the frequency had no effect on the top speed of the servos.