I have been following this thread with some interest. I know that 40 odd years ago, there was a school or two where a few of the industrial education teachers were into this sort of thing (sadly, though, NOT at the school I attended).
Maybe you can find someone with a car who will "conditionally donate" and, when it is built, it can be sold "for scrap" to a "third" party - and even the running gear sold "as scrap" to an "independant fourth party". Make sure that the "sale contracts" read that the car and other components are intended to be separated for scrap and salvage and that no representations as to anything other than it is sold "as is" and absolutely NO REPRESENTATIONS OR INFERENCES are made or claimed as any usability for any other purpose than scrap.....
THEN - If the purchaser rebuilds the salvage vehicle into ANY kind of a motorized vehicle, whether for daily transportation or ANY OTHER PURPOSE WHATSOEVER, he does so at his own risk and is solely responsible for ANY potential liability in doing so.
If getting real cash value back is an issue claim that the car was made of pure copper, which at $4.00+/- a pound would bring back thousands....
And, if your students are amenable, have then volunteer - outside of school - to be a pit crew at an El Mirage meet or two - or Bonneville.
The unfortunate trouble is that in this day and age of liability and the "it's everyone else's fault but my own" mentality, feature this -
If the school district owned a works vehicle (say - A Chevy S10) that was sold as a running vehicle to someone who decided to build it into a race vehicle and was subsequently injured or killed, the way lawsuits have seemed to have gone in the last few years, the school district could still be named as a defendant in a lawsuit as some lawyer somewhere WOULD TAKE A CASE LIKE THAT ON!... AND THERE WOULD BE SOME JUDGE WHO WOULD ALLOW IT TO PROCEED!
Sad to hear that you may not be able to make this happen....