"e output impedance of the second stage over quite a wide range - ~0.2mA - 1A", no this is wrong, what you are doing is changing the QUIESCENT current through the output tyransistors, set it to 5mA and it will work fine. If you leave it at 1A, you will over heat the transistors and flatten the batteries (if used). The output impedance is the effect when you are driving a low impedance load with a high impedance amplifier, the output voltage seems low, because it is all being dropped inside the amplifier.
This is what I do not understand, the input of a working NE555 trigger is .1mA @ 5-15V, so it is at the minimum 50K, so you do not need a power amp to drive it. You need a reasonable amount of volts, going from a good earth potential to the rail voltage. So if you want to use the amplifier in your circuit, replace the loudspeaker with a 1k resistor, and feed the live signal (not rail ) end of it through a 2mf capacitor to a 10K resistor to earth. Connect the junction of the 2MF cap and 10K to the trigger.
Frank