Sounds like a good project for a Raspberry Pi.
Get a Raspberry Pi and install Fedora or Debian on it so you can have standard OSS software and drivers for USB Webcams, microphones, a USB hard drive, and you might as well through in a cheap GPS unit for good measure. Using standard linux tools/scripts have the system mount the HDD as an encrypted disk with LUKS/encfs /etc. and have the USB+Microphone+GPS stream to the disk using log rotate to ensure there is enough space on the disk every time the system boots up.
Once you have the whole thing working install it into the vehicle so that the Cams/Mic/HDD is in the dash as part of the car. Wire up the Ethernet port to the dash so you can connect to the RaspberryPi via Samba/NFS to get the files if you need them. Then wire-up the system to a little on/off switch.
This way you should be able to record what ever you want securely, and have lots of storage space in case you need to leave it on for a long while or record multiple things. If the cops find out that you are recording them they cannot just take the disk from you since it is built into the car. In order to get at it they would need to impound the car, have someone open the dash, take the drive, and then erase it. All this would be a big hassle and create a paper trail which they would have to justify in court. Since the videos are encrypted they would have to get the password from you, again creating a paper trail to prove that there is video evidence. You can't stop them from destroying the disk once they get their hands on it. But destroying the disk after having someone at the shop remove it would look awfully suspicious, especially since the boot up log on the SD card would show that it mounted correctly.