Is anything like this even remotely possible with scripts or would that require a breaking change? Is it even possible to 'upgrade' the network to support such an option at this point?
Just send a bitcoin to yourself, and then declare that transaction is the "root transaction for My Valuable Asset."
You'd need a custom client that only accepted or spent transactions that could be entirely traced back to that Root Transaction (not hard, all transactions can be tracked back). And shows fractions of that coin as units of your custom currency. And you'd probably want to make some other changes so your users didn't accidently (or purposely) mix Your Valuable Asset coin with regular bitcoins (like a custom wallet and different scheme for generating payment addresses).