A guy nearby has reconstructed a 908 and uses a 911 powertrain. Cost has been a couple 100 thousand. I think they are forming a company to build them.
This car is a exact copy of the orginal car. He even used orginal construction processes like hand carved oak bucks and sand formed tubing bends. The body work is the same as the real cars and is thin enough to deform with a press of the finger.
You are correct about the weight, I believe he said the car came in at just under 1000 pounds. Here in lies the problem. If you EVER hit anything just a little hard head on it would kill you for sure. Really. The largest tubing on the car is about 1 inch od. No real rollover protection to speak of and plexi windscreen. None of this makes a good street car. IMHO a complete redesign of the space frame would be required to make a SAFE car. Plan on adding about a 1000 pounds to the car. Thicker bodywork, 2 in square tubing spaceframe. glass front windscreen. All in all a reshaped GTD more or less.
I am sure it could be done but it would cost no less than a startup of production of any other homebuild reproduction sports car.
Maybe a guy could start with a GTD, KVA, etc frame and make his own bodywork. Overall size/look would be close I think, My GT40 is a little bigger than the 908 I am taking about. No real room for two inside. The other seat is really a 70% scale seat with very little leg room for me. I'm 5'2". I would not consider a ride for more than 10-15 min doable. No way at speed, just not enough leg/foot room for 4 feet.
A redesigned (safer) project like this could be a pretty cool track car but my personal view is many old race cars just are not safe to be on the track with bigger heavy cars.
If you got hit by a hot shoe mustang driver he would just flatten you in a real 908. You would never walk away and you would be lucky not to burn to death. No real chance at all.