A different approach might be to rebuild the Saturn V, with modern techniques, not as a one for one rebuild, but rather take the good parts, and make them better.
For example, the F-1 engine of the first stage, (5 used, 1.5 million lbs thrust) is being reconsidered as a more modern version with higher thrust. The nozzle was meticulously assembled in painstaking fashion. It consists of cooling tubes that fuel flows through to keep it from melting. Nowadays a 3-D Printed version while expensive in capital costs (3-D printer that big for something like Inconel boggles the mind at cost) but still might be cheaper than the labour it takes to build the old way.
The J-2 engine of the second stage (5 used, 232 Klbs thrust) and third stage (1 used) has been redeveloped as the J-2X for the Constellation program and then dropped.
The overall design of the various stages is still of interest. Even if the very specific minutaue of the control systems is not.
There is no need to reproduce the identical computer systems as they used back then. Modern computers are cheaper, and easier to program as SpaceX has shown with their development from scratch of the Falcon 9 computer control system.
The trick would be not to redevelop anything that does not need it, nor to hew exactly to the original design.
Now in theory that might work. In practice, if NASA is doing it, it is hard to imagine it happening in a cost effective fashion.