The idea is to have a FM receiver chip with I2S interface to get the audio data into the digital domain as quickly as possible. The FPGA implements a ring buffer inside the SDRAM memory with an I2S to line out back end. A small controller, probably Arduino is going to to control the radio station and a small display with a all necessary information as FM frequency, rewind metric and memory telemetry. Finally the main controller, a BIG red button to rewind your radio and give superior listen experience.
The concept changed somewhat, I decided to run the analog audio rom the FM reciever chip to the audio processor and use its I2S interface as the only digital link. Makes for a much cleaner data flow.
The base platform is going to be a Digilent ARTY S7 board which provides 256MB of SDRAM already, so I don't have to do the risky SDRAM over PMOD interface. The daughter card with all audio circuit will be in a Arduino Shield formfactor for potentially later re-use.
The design and layout is finished, schematic (with fixes) and assembly drawing are in the files section.
And to fill in some gaps: With 256 MB of memory all used in one big ring buffer and assuming 44.1 kSamples/sec, my math adds up to just under 25 minutes of rewind time, which should be plenty.
You could also use RDS to implement commercial skipping.