On a technical note, I wouldn’t really say the transactions are “instant”. In fact, closer to the opposite, they’re (almost) unbounded in time (nearly asynchronous). In practice, it turns out that it’s “faster” than other cryptocurrencies, especially those base on the proof-of-work model, but it’s a far cry from instant also.
I don’t know if that affects the idea you had in mind, but thought it was worth noting.
Can you offer a bit more context for this? Do you mean copying the SafeCoin ecosystem as in creating a new Safe network yourself or creating a DApp with its own currency on the Safe Network? If the former is what you mean, see this thread on the existence of potentially multiple safe networks. It would essentially mean starting a few nodes of your own, convincing people to join your Safe Network, and building from there.
That said, the paper you linked is a bit dated. You may want to read the other papers in that repository as well as take a look at the RFCs that have been proposed. There have been many changes since that paper was published, and the paper is rather high-level in any case.