Do you have access to a high bandwidth oscilloscope? do you observe the expected exponentially decaying pulses? Sound like you could debug your circuit to find out what is happening.

For higher energies on would want to use a thicker intrinsic region, one approach I have considered would be to use a distant aperture, so that the direction of incoming rays is known, and then tilt the photodiode so that the rays can experience a much longer path in the intrinsic region (so that when a photon generates a high energy electron, the stopping length can be attained without clipping / aliasing the energy resolution as much). Basically tilt the photodiode so that its plane is closer to parallel (or exactly so). There is a trade off between cross section (fewer events) and maximum energy measurable, one can compensate for the lower cross section by having more photodiodes.

all 3 proposals would be passive, including #3, so it wouldn't emit X-rays, just detect them and build up a self-consistent picture that explains the observation statistics for each event (with that energy and time/orientation of the silicon wafer).