Hello Rob,
Get familiar working your handstrikes from both leads. First do them from the clock drill, delivering them from 12:00 / 3:00 / 6:00 / 9:00. Once that feels comfortable start to work from a boxing style structure. Check out the UC videos, a lot of good drills are outlined there.
First get familiar with the old boxing series.
jab
jab, cross
jab, cross, hook
jab, cross, hook, uppercut.
After that start to deliver your other handstrikes from the same structure "example"
finger jab
finger jab, palm strike
finger jab, palm strike, hooking elbow
finger jab, palm strike, hooking elbow, upward elbow.
Start there, and when you get the hang of that, then start to work them from movement.
have your training partner move around, and flash the mitt to you, you need to hit it with the apporpriate hand technique.. Get a little creative, and think of variations.. Before you know it, you will have a ton of drills to practice.
Remember, someone made up all the common drills practiced all over the world.. you too can create!!
Keep up the hard training.
Dean.