Are you chasing a ZL1 1LE? Please tell me it's not an SS
A ZL1 is a pretty incredible track weapon. No shame in being a little slower than that. Assuming he's also not a better driver, you might need a couple more mods to catch up. A tune and exhaust (when available) will bump you up to same power level and more (650-700).
You can also wait for Team Schirmer axle kinematics and suspension. They're going to be lethal but not cheap.
Try 305s in the rear and see how it grips
I feel like with the amount of laps you're doing, you're going to go through a bunch of pads/rotors regardless of car, especially at this weight. Same with tires.