OK. But that doesn't change anything. The attacker still can fake everything, with the exception of 1) the blockchain until the fork, and 2) the stake he has at the moment of the fork.
Let's see an example for one block of the fake chain, if he buys 51% of the keys at the moment of the fork:

Block 1:
- He calculates a PoS hash with the coins he has. That should be no problem, as he owns 51% of the stake.
- He creates a block header with a timestamp that's inside the allowed "target spacing" range, starting from the pre-fork block. He has total liberty to fake the timestamp, so he can use the "ideal value" to avoid that difficulty decreased.
- Instead of the original transaction that gives away his stake, he creates a double spend transaction to an address he controls and includes it in the block, so he continues to own 51% after the block.

Block 2:
- He calculates a PoS hash building it on Block 1, with the 51% he owns.
- He again fakes the timestamp, with a value inside the ideal "target spacing" range. Difficulty should stay high enough to be higher than the "honest" chain.

Block 3-X: Rinse and repeat until the chain has caught up.

What you're referring to is an analogy to PoW, but it doesn't work in PoS - the attacker has all the time of the world to create the PoS hashes, because with 51% of the stake he will eventually outrun all other stakers due to his drastically higher coin-age value, even if he starts to create the chain a whole year after the fork.

I decided I can't do that (like Craig Wright ). It's simply not so important for me to waste an enormous amount of time I don't really have. (And now I'm only playing the Devil's advocate, because I'm not part of the anti-PoS fraction.)

But the above example should be enough. You have to prove now why the attacker cannot fake one of the steps I detailed.