I would do it afterwards as well. Stiffening the floor shouldn't be a problem since the car needs to be on it's wheels (or simulated). Unless of course there's no drivetrain in the car (ie, it's light).
Here's a story I did a while back on the install:
http://www.popularhotrodding.com/tec...ors/index.html
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"A ship in port is safe, but that's not what ships are built for."
See Bad Penny run the cones:
https://www.youtube.com/watch?v=8GUPPIX-92U
1971 Chevelle Wagon - Roadster Shop Chassis ProCharged Shafiroff LS and lots of yada yada
1968 Camaro - Project Track Rat - 440 RHS LS