I get the gun back on target quickly enough but it takes too long for me to reacquire my sight picture. I have to let the sights "settle" longer than I'd like. Typically, is this a grip issue? Stance?
Typically, it's a confidence issue more than anything else. As long as you have a secure grip (aren't letting go with your non-dom hand after every shot, don't need to readjust your grip all the time), and as long as you are snapping the gun back to the target quickly to manage the recoil, then your delay is almost certainly a confidence thing.
If you've gotten in the habit of waiting for and then "snatching" a magic moment when everything is absolutely perfect, it can actually slow you down even though each individual shot will feel fast. Instead, what you need to do is accept the slight wobble in your sights, accept imperfection while continuing to realign the sights through the wobble, and press the trigger smoothly.
Here's one of my favorite learning to go faster drills: http://www.corneredcat.com/the-speed-up-drill/
It's good because it improves both speed and
trigger control. Too many go-fast drills teach one while destroying the other.