That sucks. I don't think it's ice mode though, it's probably trying to keep you from spinning due to brake + steering inputs. Makes sense it's less severe in the ZLE due to the OEM 3R tires having more grip.
Do you think initiating braking with less steering input could solve the issue? I know it sucks to have to adjust your driving style to suit the car, but tons of folks track these cars without incident. I do think you should have bought a ZLE to begin with, but it's a bit late for that.
Maybe it's just time to move on to a real race car. I recently saw Camaro GT4Rs on sale for $125k. I wish I could afford one! I've driven one in Automobilista 2 on my Fanatec sim rig, if that's anywhere close to what it can do IRL it's capabilities are likely far larger than anyone's balls, assuming they aren't a pro race car driver. Bonus is it still has remnants of an OEM interior, so if you can get a VIN from a wrecked Camaro and use that to register it via salvage title, it'd also be CAM-C legal.