Welcome To TFL
Incrimental gains are still gains so good for you in that respect. I know alot of folks have limited range rescourses therefore not everyone gets to shoot at a moving target. With that said moving while you shoot at a stationary target can make a difference too.
Obviously range rules dictate what you can and cannot do so I would speak with a range officer before you try any tuck and rolls. Better yet save the tuck and rolls for the movies. Advance on the target while shooting then back away while shooting. Step side to side and continue to address the same target.
If you have a private spot to shoot you can go mad scientist however I suggest doing so in the company of a range buddy to offer you assistance if you need it.
Again welcome to the boards, Vermonter