If your car has OEM "ZR" tires, they'll be fine. Don't worry about the stated width restriction - if they're the original tires that came on the car - they're acceptable. Otherwise, they just have to be rated (H, V, W, Y, or "ZR") for 130MPH or more. You don't need any fancy LSR tires. Some actual "competition class" cars even run street tires - provided they're rated for speeds above their existing class record.
A bigger problem is likely to be the requirement for metal valve stems and caps. TPMS-equipped cars (2007 and newer) generally have rubber valve stems. I suppose you could just have the metal ones installed, but it's actually illegal for tire service providers to disable TPMS. And, you'd have that stupid idiot light on (and perhaps even flashing) if you did. Additionally, if your TPMS is disabled, you'll probably lose any ability to turn off traction and/or stability control. I've even heard that newer sensors can't be tricked by putting all of them into your spare tire (or a single pressurized container), either.
I face that same problem, as I plan on running my new car in the 130MPH Club this year. The good news is that Tire Rack (and probably others) has TPMS sensors with metal valve stems. The bad news is that they ain't cheap. I ordered mine Friday, and the set of four is about $180.00 shipped - for a Ford. Then you'll have to have the new sensors installed and have your car reset to trigger them, as well as another mount and balance job. So, the cost for metal valve stems will be near $300.00!
Thanks to some idiots (plus their lawyers and Congress) who rolled their cars because they didn't check their tire pressure, we're stuck with this crap!
So, I'll have to reject your car if you come through WoS Tech with rubber valve stems.