So less assume there are no checkpoints to block it.
If the Main Chain is 3 months ahead of your fake chain, (because you purchased old keys)
Detail exactly how you are going to fake the time stamp on your fake chain blocks.
That's simple - you only have to write the corresponding number at the place in the block.
You can put any number there.Doubtful, but I like to see you try it.

Especially curious to see the effect on the difficulty #s.
Detail exactly how you are going to fake the required time & hashes between blocks so it's difficulty # matches or exceeds the main chain, while also exceeding the block height.
Difficulty only matters in PoW chains. The attacker only needs to ensure that he has more than 50% of the weight ("chain trust" called in Peercoin) at the moment he forks his attack chain.
He achieves this with a double spend - instead of the original transaction of the "old key owner" he places his own transaction in the first fork block, which spends the same coins to another address he owns. From this moment on, both chains become incompatible, but it's trivial to produce the matching block hashes.
Your Fake chain has to exceed the length of the main chain and has to have a higher difficulty level for it to be accepted over the main chain.
You refer to "chain trust", not to difficulty. If you own 50% of the stake in your chain, then it's trivial to achieve high chain trust values.
I am referring to difficulty, in Proof of Stake it is the # that increases or decrease to make certain the blockspeed is maintained.
It is also part of the security in some Proof of Stake :
hashProofOfStake <= [Coin-age] x [Target Difficulty]
[Coin-age] = [amount of coins] x [days in stake]
Calculating a fake chain should be no problem. If I have time I could do that with a short example, but don't expect it tomorrow.
It has been ~2 weeks now , any progress?