If each of the modifications is an Actor, and the Actor applies its changes to the world, then all you need to do is make sure that you re-create the same Actors in the same order, and the world will be re-created for you.
For small games in a small world, you can probably even do it without worrying too much about the necessary low-level optimizations, as long as the basic “periodic checkpoint” is still there.
I don’t know exactly how far you’ve gotten with the “actually modify the world” logic – if you have that working, turning that into networking should be possible.