Break out the welder, Tony! At least that or some Fusor adhesive. Those floors are:
1. Stressed panels helping with the structural integrety of the car/chassis/suspension/flexibility.
2. What holds "you" in the car. Major safety consideration - probably more than the cage.
3. Very structural in an accident or wreck. See #2.
4. You might not even pass a safety inspection with the floor only "riveted on". Especially in vintage racing. See #2 and #3.
5. Alot of the guy's your competing against are watching your every move with this car.... Do it right... Don't give them anything to file a complaint about. See #'s 2,3 and 4.
At minimum, at least "fusor" them in. But I'd go with Welding them!!!!!!!