Hi Tammo,
You could look at using the Convergent Design Flash XDR as an onboard recorder: it records a HD-SDI source to solid-state CompactFlash media at very high quality (MPEG2 4:2:2: long-GOP up to 100Mbps, I-Frame only up to 160Mbps). As it's all solid state with no moving parts it's impervious to vibrations and G-forces.
As you point out the most likely issue you're going to encounter here is size constraints, given how cramped on F1 cockpit is! The unit itself is fairly small for what it is, 8"x6"x2.5" and weighs just under 1.2kg. It runs off 6-20V DC, with a 4-pin XLR connector, so you can power it from a range of batteries. The XDR has been used in sports cars, rally cars, on motorbikes, jet fighters and stunt planes, so its not outside the realms of possibility to use it on an F1 car!
http://www.convergent-design.com/CD_Products_FlashXDR.htm
Paul