Shawn,
I haven't had a 69 camaro in many years so I can't be of much help regarding the tire fitment.
A few questions regarding your engine set up I believe are in order so that we can provide the best nitrous info possible. What have you done to the 406? It sounds stout, but did you choose the right parts when it was built? I would hate to suggest that you try a 250 shot only to later learn that it has a cast crank.
Assuming it was built with the right stuff, I see no reason not to run a healthy shot of 'go-go' juice through it.
Tell us more about it and I am sure that the nitrous junkies on this board will be more than happy to add their $.02 worth.
Many Thanks!!