That definitely would work for Earth today. But note that to simulate observers on Earth today, you had to simulate from the big bang up to (today - light-crossing time from body) for each celestial body.

That's significantly larger than Earth, only to simulate Earth today, because tomorrow the entire universe would go dark.

Lightspeed gives structure to the computation of the universe but it doesn't reduce the load.

Saving templates doesn't reduce the load either, not in the sense I'm considering. It may practically mean that you don't have to run it again, but theoretically if you want to know how much computation got you to this point then you have to count the computation of the templates.

So if you had our whole universe at your disposal, and knowledge of all natural laws and processes, and knowledge of the starting conditions, and absolute power over matter and energy, you still cannot simulate our entire universe with anything less than just restarting it. If you wanted to simulated it specifically for some observers, you can free up resources using the lightspeed method but that's a computational debt you cannot pay if you wanted the simulation to continue.