Write, just write. Don't stop doing it. Find a reason to do it everyday, for notes, for reminders, write letters to people -- which seems to be a lost custom in Western countries. If you do not like your handwriting, copy someone else's. Change it to make it comfortable for you to write.

> I’m fairly certain that simply practicing the art regularly would improve things...

This.

> ...any guided drills, programs (digital or otherwise) or any iPad apps that would assist in this?

Not this.