"i need one with training wheels! never could drive those things in a straight line"
Its like my dad always told me, you've got to keep the handles low and level and you'll be fine. If it starts to tip, since you have the handles low just let it down.
If you try and go around a turn and unlevel the handles so it leans, sure its easier to go around the turn but if you have a load its all going to fall out

So the best way to turn is to turn with your hips and butt, reposition your whole body, instead of tipping the handles and shifting the load.
I've flipped a couple of these
wheelbarrows full of cement over in my days
Walking with the WB backwards up a hill sounds like a great idea, and depending on the pitch of the hillside it could be really grip intensive.
If you had a retaining wall around your house or something you could practice picking it up and loading it over the wall.
The rougher the ground is, the more its going to work the traps and triceps as you try and stabilize it.