I think it's best to handle all the math is in the FPGA (but I don't know FPGA). That way, no need for a peak detector or RC circuits, and it’s a lot easier to fix code than it is to reroute a PCB.  Also I've tried to choose easy to solder chips:

• MICROFC-60035-SMT-TR1 as a sensor
•  LTC6268 as transimpedance amplifier
•  LTC6363 differential amplifier
•  AD9226 fast "and good?" ADC
•  iCE40HX4K + SPI flash for data handling
•  maybe some STM32 for communicating with outside world

TBD:

•  SW tools for iCE40HX4K 
• divide project on what can be done in v1 vs what can be touched in v1, learned and finalized later.