The problem with using someone else's privkeys is that they can still have the same privkeys and undo anything you can do.
They also have the same actual coins you'll be using on your fork.
So even if you control enough stake to generate every new block,
there is still equal or greater stake on the main chain that can do the same thing.
Of course, but it isn't coordinated. If I have a majority of stake, enough to generate every block I can coordinate my attack much better than the set of uncoordinated honest nodes on the network. I'm fairly sure this is equivalent to a 51% attack and there is nothing which can be done at that point.
Therefore, everyone would know that you want those specific keys for an illegitimate reason,
and then they would either refuse, or find a way to get your money while anticipating and preventing your attack.
You're assuming that regular people need to know the inner workings of blockchain consensus - this is not a reasonable thing to expect, IMO.
In order to create a significantly longer chain, you'll have to present a chain of valid blocks that are timestamped to appear faster than the sequence of blocks on the real chain. Have you run any numbers to estimate how high you'll be driving the difficulty to squeeze those extra blocks into the same period of time?
Timestamps can be faked; as long as the fakery still fits within the acceptability window, online nodes will accept the fork. Offline nodes have no way to tell, and will accept the fake fork regardless.