It really shouldn't be that hard for handball penalties. You can tell when someone deliberately handballs it, everyone that's played and watched football has a good idea of what's deliberate, so let's say the first question is:
Did they deliberately move their arm to handball it? If yes pen, if no, ask the following questions and award based on the answers.
Did the ball striking their arm/hand stop it from reaching an opponent in a position to score?
Did the ball hit their hand after ricocheting off another part of their body or from less than 3-5 yards?
So Egan Vs Villa
Didn't deliberately move his arm
It did stop a goalscoring opportunity
It didn't ricochet off him
2/3 Penalty
Ours Vs Burnley
Didn't deliberately move his arm
Did stop a goalscoring opportunity
Didn't ricochet off him, wasn't from point blank range
2/3 Penalty.
I think that's a pretty fair system, balls through a crowd bouncing all over wouldn't be given, you'd still have to count on refs judging unnatural body positions though, but at least we'd know the criteria with something like that.