Beyond a doubt, the probable #1 issue that will get you is the low clearance, especially the 427 Cobra's front
Oil Cooler and
oil pan. Steep inclines, debris on the road, parking bumpers and curbs, etc will take out the front
oil cooler very quickly.
Keep a good distance behind other cars so that debris in the road is visible long enough to react and avoid it. A thrown tire tread/retread or dead animal in the road will do much damage to the front of your car while "normal" cars will pass over it without a scratch.
Remember to take steep inclines (up or down) at a 45 degree angle, especially tall lips to driveways and even some speed bumps.
Lastly, some of the higher powered engines can do some pretty good damage to drive train components so do NOT pull 5000 RPM and dump the clutch.
Find a good big parking lot that is empty and preferably WITHOUT lamp posts, and start going around in a circle and keep applying the gas to get the feel of when and how the rear end will slide out. Try this both clockwise and counter-clockwise. This is the best way to get the feel of the car's limits easily. You can get dizzy though. You can learn to slide out the rear with the throttle.
If you vary the tire pressures front and rear you can tune this reaction to some extent.