What about using a sample and hold in sync with the switching power supply to sample the amplifier output when the waveform is undisturbed?
The TIA doesnt reach a steady state due to the high current pulse and the high feedback resistance
One could try adding an electronic switch to connect the signal to ground and maybe also isolate the integrator.
But how to design a switch with a low off-state current and fast switching capability? The input offset of the OpAmp causes a voltage across the transistor, therefore several nA current flows. The body diode could also cause problems.
you only need a dv/dt of 16.6 V/second to get 50pA
Can you post the schematic of your TIA?
Until now, its just a TIA like this (+Capacitor in parallel to the feedback resistor)
https://upload.wikimedia.org/wikipedia/commons/thumb/f/f1/TIA_simple.svg/400px-TIA_simple.svg.pngIts a High-Voltage Source with good decoupling/ filtering. Voltage seems to be stable after switching, I will measure it again soon.
What you can do instead though is clamp it from the output to the inverting input either with a low leakage FET or low leakage diodes. Transistor base-emitter junctions make good low leakage fast diodes.
If the high voltage edge is consistent, then charge compensation with another edge and capacitor could be used.
But it needs to sink and source charge due to the positive and negative pulse. For this, the diodes would have to be connected in antiparallel. Wouldn't this lead to an undefined gain?
Charge compansation is the right Keyword. In fact, the waveform does not have to be inverted exactly. With a calibrated compensation voltage this could work!
The OP hasn't mentioned what they are trying to extract from the signals, if its just the DC then there are many other options.
Its "just" the DC-current

What other options do you have in mind?
Photorelay across the feedback resistor, trigger when output voltage exceeds positive/negative threshold?
I've been thinking about that, too. But most photocouplers are too slow (turn-on/off time up to some ms) and the off-state current is much higher than my measuring range. Could not make it work.
Many thanks for the helpful answers!