As I understand it, Aragon is a way for a traditional company to sort of 'blockchainify' itself, by putting board management, funding, accounting, etc. of a traditional organization into a dApp.

Colony is a really fundamental re-imagining of the way an organization works. Instead of being a normal company ported to the blockchain, a Colony is an organization native to the blockchain.

Not so - a blockchain or other type of decentralized shared ledger is required for the reputation system to work as it should. Reputation needs to be calculated and verified so that it can exist independently of some sort of gatekeeper or platform (as you are implying).

Tokens on the network also are essential for Colony governance (voting, dispute resolution, dividends/rewards, etc.) - This is why Colony is built on Ethereum.

Colony is beginning Beta II this quarter; if you have a use case and don't mind providing some good feedback and tolerating occasional bugs, send Collin an email to inquire about participating.

Currently the software is closed-source, but will be opened up when it's ready.

The whitepaper was just released last week, and the Colony dev team is working on getting a good foundation for the contracts that will comprise the Colony network - once those are ready, it'll be opened up.