Made good progress with operation "fling a bunch of cars", so I'll gladly share the results!
Since the first iteration, I have added...
In the following GIF, if you focus on the hand you can see it open and close, as the character changes size. Just wanted t make sure the grip looks somewhat convincing – it's a very rough approximation, but better than nothing!

The same goes for the "pick up" animation: It may not be obvious, but there is actually a lot going on, to make it work and look/feel nice. It's never going to be perfect, but I'll gladly settle for "good enough!"

Overall, I was actually surprised how smooth it was to set this up: I haven't messed a lot with inverse kinematics in Unity yet, but they're not as scary as I originally thought they'd be. Still, if I wanted to polish it all the way, I could probably spend the rest of the year tweaking parameters in the animation blending, IK weights, etc. – so, let's not get carried away, haha!
What's still missing?
I'm really happy with where this feature is, already. But, of course, there is a bunch of stuff still missing, before it's actually complete and finished.
Some of the most important things on my list, right now:
So, there's still plenty to do!