Maybe I'm missing something, if so, i apologize for the rest of this post.
Sounds like you're not leaving much of a safety margine. 1140x2=2280lbs. Let assume your car, with you in it, has a front weight of 2280lbs or slightly less. I can't answer this for sure cause I have not put mine on my scales yet. Are you still good? Your car sitting with you in is not 50/50 front to rear distribution. How much weight shifts to the front tires when braking at the track? Willing to bet you will exceed the weight rating of those front tires. But what could go wrong with under rated tires at over 140mph?
Believe me, I thought about this because you are right, the street radials are a very heavy tire compared to the race ones I use on my other two race cars. However, they are rated at 1650lbs each. I just didn't feel the weight savings was worth the risk. Remember, there is another racer in the other lane. Sorry for the soapbox. Good luck and be safe!