Yep, the real challenge now is how to spend it all without getting caught!

This is what I don't understand. If you can watch every transaction, is the key to successfully getting away with theft the ability to withdraw funds without being detected?

You can just pass it through mixers to anonymize it.

Input 1,000 different peoples coins, output any one of their coins one at a time. There's no way to know whose coins are coming out the other side.

https://en.wikipedia.org/wiki/Bitcoin_mixer

Something like that yes.

You can try to conceal your coins by sending to many addresses, using mixer services to switch your coins with someone else and then trade them often to other cryptocurrencies which makes them harder to track. I would personally try to trade them for Monero where you basically can't trace your transactions.