I have probably spent more than 100 hours stuffing dummy rounds into my shotgun then just racking them right back out.  I practice both loading the tube and loading from an empty chamber with the bolt locked back as well as loading then manipulating the action as if to load the gun and/or clear a malfunction by rapidly working the bolt without losing my cheek weld and sight picture.

As far as live fire drills I always start every shotgun practice run with a loading run.  I start with an empty gun or maybe a gun with one in the chamber and load it full all while moving left/right/back/forward/kneeling/sitting then I shoot 4-8 and reload it again.  Every live fire session always incorporates as muck loading as shooting.  Actually most times I load more than I shoot cause loading is free and shooting costs $.20 or so per bang.  

I don't have a particular shooting drill I could give you that will make you a top shotgunner.  I find shooting the shotgun and hitting the intended targets to be the easiest thing we do in 3 gun.  The hard part about 3 gun shotgunning is knowing the pace at which you can still engage and hit all the targets.  So to work on learning that pace I shoot a wide variety if targets shapes and sizes that are spaced closer and farther apart.  I want to know how it feels, sounds and what my sight pictures are going to look like when I engage a plate rack at 7 yards as compared to at 20 yards.  Or a set of 4 full size poppers compared an array if 4 5" square steel on stands.  Once your eyes know how fast your body can engage the targets then repetition increases your speed.  Lots of repitition!  I keep track of every round of what caliber I am shooting HERE so I know if what I'm shooting translates to better match results.