Hi,
Before we talked about V_ce of the first bjt (to safely switch OFF the second bjt), now you talk about the V_ce of the second bjt.
We have no information about the second bjt's collector current .... with 0.1mA there wil be no problem ... with 100mA it's about impossible.
Why do you want it to be < 0.2V?
Still no information why not use a mosfet, which easily could satisfy all the given reqirements, because it has a huge current gain.
It seems the requirements change from post to post...timing, currents, voltages...
You know, I'm a friend of deciding the requirements first, then do the design.
Maybe you could tell us what the whole circuit is good for..
Klaus