bjt inverter for dc signal
Is there anything wrong with it or can it be improved?

As I stated in the comments, the circuit appears to be transistor-dependent. If you build up this circuit in practice, you may exchange the transistors until you find the required behavior.

I can't spare more than 1 opamp, and I couldn't figure out how to do it with just 1.

Well, all you need is a DC amplifier with a gain of approximately -2V/V. It's quite easy with only one opamp:



simulate this circuit &ndash; Schematic created using CircuitLab
I used an LM358 here but you can use any other opamps you have at hand.
The input stage with complementary transistors acts as a buffer with restoration (to compensate the VBE drop). So the voltage at the emitter of 3906 is nearly equal to the input voltage.
Without C4, the following stage is just an inverting amplifier. And the gain is \$\mathrm{A_V=-(R2/R1) = 2.2V/V}\$. The addition of C4 in parallel to R2 makes the amplifier a 1st order active low-pass filter to reject any AC components (above \$\mathrm{(2\pi \ 150k\ 1\mu)^{-1} = 1Hz}\$). So the circuit amplifies only DC.