I have actually tried the platinum trophy, and I was able to do it with a grind. Some discount, drones, and habitat events should help. The 10 billion trophy takes much more EB, but you should be able to acquire those 10 prophecy eggs from the first 4 trophies. Don't worry if you can't afford the habitats or research, your population will grow and you will get more money.
(You also don't need any artifacts at your EB., but it may be a bit more of a grind.)