Offset problems with charge amplifier
In Spice, I just put a capacitor in series with the voltage source to
simulate the stuff.

This is probably the wrong way to simulate the circuit. The normal way is to use a current source in parallel with the capacitance of the accelerometer. What value source capacitor did you choose for the simulation?

The accelerometer has roughly a capacity of 5nF. Therefore I have
chosen this. Is this wrong thinking? Oh, that would be embarrassing

Well either you have the red face or I do but firstly, we should look at the reasoning behind your dc feedback network. I think you have gone for the 5000:1 attenuator so that you can choose a 10 MΩ feedback resistor so that input bias current effects are minimized. Looking at the op-amp data sheet, the bias current is worst case 10 pA at normal temperatures and through a 10 M&amp;ohm, resistor, this will produce an input voltage offset of 0.1 mV. The feedback resistors provide a gain of 5000 so that immediately puts the offset output voltage at 0.5 volts and it's becoming problematic.
Changes in temperature of the device could make the offset input current 2 to 10 times worse and this is probably what you see.
So, back to basics (with me being prepared to be red-faced), use only unity gain feedback; maybe 15 MΩ: -

The AC response is now this: -

And that looks OK to me.
The transient response for frequencies of 0.01 Hz, 0.1 Hz and 1 Hz (all superimposed) with an excitation current of 0.1 μA is this: -

This is how I would set-up a simulation to design a charge amplifier and it's how I'd analyse the op-amp's input current in order to decide on an adequate DC feedback system.
Of course, I'm sticking my neck out but I thought you appreciate some tangible help even if I missed something important.

Following further conversations, it looks like the feedback capacitor needs to be significantly higher. Here's an AC response using a single 100 MΩ feedback resistor and variable capacitor: -

The problem is the limitation on open loop gain. In the picture above, I simulated using an OP4177 device and it's model has an open-loop gain of 100 million (160 dB) but this is not what you will find with most op-amps.
So with red constraints at 0.1 Hz and 10 kHz and a purple constraint at 160 dB, all you can play with is the feedback capacitor and it looks to me like 20 nF (as opposed to 20 pF) is viable but only if you can get an op-amp with this extremely large open-loop gain (160 dB). Typically, you'd be lucky to find a suitable op-amp that is much more than 10 million and then you are constrained to using a bigger feedback capacitor like 200 nF or even higher.