Maybe, this is my level of misunderstanding. If I am starting with 54V and I want the circuit to provide a maximum of 54V go feed the current across the slice such that it follows the voltage from near 0 to about 2.3uA (i.e., the actual voltage across the slice is unimportant, it is the current that is important). My battery current source is obviously not a problem so I think there is something fundamental about the operation of a transistor that I'm not getting. Sorry for this, as I said way above, my level of understanding of how electronic components work is probably interfering with me seeing the forrest because of all of the trees. It is nice to see, a design that could work that doesn't use an op-amp.Okay you wanted transistors.
Below is the LTspice simulation of a transistor amp whose output goes from 0V to near the supply voltage for a 0-5V input which uses feedback to give a stable gain of slightly over 10.
A three transistor complementary circuit is used to get sufficient drive for the desired output load with low quiescent current.
The gain is approximately R3/R1.
View attachment 91347