TiVo-like device for live FM radio

I have an ambitious project in mind, something like a TiVo for live FM radio. I am inspired by the cheap stereo FM radio modules available for sale like this one:

http://www.ebay.com/itm/FM-Stereo-Module-Radio-Module-RDA5807M-RRD-102V2-0-Wireless-Module-for-Arduino-/311563537161

There are different ones available, and they are so inexpensive, I could try different ones until I find a favorite and still spend just a few dollars.

What I would like to do is record the output in stereo and play back in real time the audio I recorded a few minutes ago. Does anybody know of a module that will handle that, recording into a circular buffer, and play back at my choice of time in the past? I would like to jog forward to skip commercials or jog back to listen to something again. I think if the module had 100 or so MB memory it would be able to handle recording 20 to 30 minutes or so of CD-quality audio.

I think I am comfortable with figuring out the interfaces between the components, programming, human-interface (what buttons do what), audio switching and amplifying, and FM tuning, just don’t know a good and simple way to control recording and playback of good quality stereo audio.

I will start out with one station and a simple interface, and add the ability to record multiple stations at the same time by adding more sets of components and making the user interface more complex. I may eventually add the ability to dump the current contents of the recording to a separate device or upload to cloud storage, or record and save shows at specific times on specific radio stations.

Ideas anybody?