Electronic – Some questions about using h-parameters to model a BJT

I don't now if your simulation is correct, but you could make it less beta-dependant by increasing negative local feedback, by for example emitter degradation, such as increasing R1 and R2.

By using a Darlington or Sziklai pair, R4 and R5 can be increased while still maintaining output current. Discussion of thermal properties: https://sound-au.com/articles/cmpd-vs-darl.htm#s4

If some crossover distortion is acceptable, the biasing voltage could be lowered so that the quiescent current through Q1, Q2 is 0.

One important component in the circuit is the output capacitor between RC and RL.

At power up it will charge up to the DC voltage present at the collector of the transistor and from then on will act as if it was a battery and keep a constant DC voltage across it.

When the transistor takes more current as a result of the input signal it will cause the voltage at the collector to drop and this will be transferred through the capacitor to the load RL.

Since the assumption is that the capacitor voltage remains constant the voltage at RL will go negative. (below ground)

Similarly if the transistor current reduces the voltage at the collector will go positive and this will be communicated through the capacitor to RL which will then go positive relative to ground.

In order for the voltage across the capacitor to be unvarying the time constant of the capacitor and RL must be much greater than the period of the signal being amplified.

This type of "capacitor coupling" is common in amplifiers where the DC component of a signal is unimportant such as in audio or RF amplifiers.

The capacitors at the input (C1) and on the emitter will also have been selected to be large enough that the voltage across them remains constant for a complete cycle of the signal.