coolchip,
You might be able to find an old radar intruder alarm sensor, these were quite common before good body heat sensors become popular. These have most of the needed electronics on the main unit with the transmit and receive horns. They are doppler (so detect movement towards/away from the radar, rather than giving a distance measurment) and give a signal proportional to the velocity. You might be able to redesign them for pulse mode, certainly you have all the main necessary bits already made.
For a nice demonstration, I would imagine they are ideal. They come up on eBay every so often, one day I might get one myself. I used to play Paintball and always wanted a small, portable radar to detect incoming enemy.
I can't find a complete one on eBay at the moment to show you, but someone is selling one of the horns removed from the complete module.
**broken link removed**
Hope this gives you some ideas,
FoxyRick.