OK, this I pull out from my butt!!! No guaranty it will work, but at least you can try:
Attachment:
Output stage.jpg
To gain more voltage swing, I use common collector on both top and bottom.
1) I roughly calculate the resistor value so I get 0.4mA current on the input chain that drive the base of Q1 and Q2. ( R1, R2, R3 and R4).
2) This will give about 0.8V across R1 and R4.
3) 0.8V across R1 and R4 will make Q1 and Q2 conduct about 5mA. But it's likely not balanced and the output voltage will swing to one rail or the other.
4) R5, R6, C2 and C3 form a negative feedback. If Q1 conduct more current than Q2, then the output will swing up. But then it will pull the input junction up also and decrease the drive of Q1 and increase the drive of Q2. This is negative feedback to keep the output roughly about 1.5V ( half way between the two rails).
R5 and C2 and C3 create a dominant pole for the closed loop DC feedback of pole frequency fp= 1/( 2pi X 5.6K X ( 220uF/2)) = 0.26Hz.
But this is just guessing, too much work to do detail calculation and deal with stability. Think about this circuit to make sure it works. I am just going through the thinking with you. If this works it will definitely give you the maximum swing with such low voltage. If you can use MOSFET, that would be much easier.
This stage do have gain. the gain is about (2/7.6) X -10 = -2.63.