They can design it so that the firmware is in two parts.
The first part does minimal initialization and then gives control to the second part, which is where most of the functionality is.
The first part is also the part responsible for implementing the firmware update protocol and the reset procedure. The first part would either not allow any update to replace the first part, or it would only allow the first part to replace with factory signed firmware.
Alternatively (or in addition) they could have a diagnostic connector that lets external hardware read the firmware memory. You could then do the factory reset on your used car, and then hook something up to that diagnostic connector and have it compute a hash of the firmware that you can check to make sure it is the right firmware. An Arduino should be sufficient as the thing to read and hash the firmware.
I think the best solution would be your first one, but have the second part be stored on removable media, like an SD card. Make it physically impossible to write changes to anything but the SD card (e.g. use actual ROMs for the first part, and use volatile RAM for temporary storage of the code loaded from the SD card).
Then, if you want to be sure that the firmware isn't hacked, simply remove the SD card, put it in a computer, and verify the contents. If paranoid, overwrite the SD card with the official firmware. If extremely paranoid, throw away the SD card, buy a new one, and write the official firmware to it.
They could still open source the first system's firmware code. FOSS doesn't imply easily modifiable, does it?
E.g., rms says he used a Lemote Yeeloong because of its free BIOS, but AFAIK he couldn't have reprogrammed it unless he removed the BIOS chip from the motherboard.
The first part does minimal initialization and then gives control to the second part, which is where most of the functionality is.
The first part is also the part responsible for implementing the firmware update protocol and the reset procedure. The first part would either not allow any update to replace the first part, or it would only allow the first part to replace with factory signed firmware.
Alternatively (or in addition) they could have a diagnostic connector that lets external hardware read the firmware memory. You could then do the factory reset on your used car, and then hook something up to that diagnostic connector and have it compute a hash of the firmware that you can check to make sure it is the right firmware. An Arduino should be sufficient as the thing to read and hash the firmware.