Water Pump problems of the 2011 Chevrolet Equinox

Hello, the vehicle is under 60,000 miles. I received a recall notice for the malfunction light. After diagnosis, it was reported the car burned oil and caused oil sludge. Many reports are needed to be replaced, including the pistons and rings. The cost of the job is between $4500 - 6000. Gm will not repair the car under the bulletin, 15285c. Apparently, the car VIN is covered; however, gm will not repair because I can't proof changing oil every 5,000 miles. I do have service provider receipts dating back to 2012. I couldn't proof changing the oil myself. I have completed this tasks in addition to the service shop. Gm reported the car to burn oil excessively at 2,000 miles. I wasn't aware of this until 2016, five years after time of purchase. I'm disappointed with gm not backing their product. The car has the following issues due to this recall. -lunges at idle -stops at idle -sounds like a ticking time bomb I have already invested $1200 in the engine fixing the timing chain and water pump. Attached is a conversation saved with gm support. Thanks, chad.

Initially the issue started with rough idling of the car, engine ticking, and engine stalling. After indicating this to the dealership, they informed me that the ecm needed to be reprogrammed because the oil life indicator was not properly calibrated causing the system to think that there was more life on the oil than there actually was. The engine balance chain eventually broke while on the interstate (55 mph), due to improper oil lubrication. The fuel pump, water pump, and a few other items had to be replaced due to the damage caused when the chain broke. I notified the dealership once again after engine ticking/ rough idling re-occured and they indicated to me that the engine ticking during startup was normal. The engine ticking progressed to becoming a constant noise. I noticed that when I took the oil in for an oil change, approximately 2000 miles in, that the oil dipstick would come up completely dry. This indicated the vehicle was experiencing an excessive amount of oil consumption. I took the vehicle to the dealership who indicated that pistons had to be replaced and the exhaust manifold was cracked. This indicated that the engine was observing some excessive amount of heat most likely due to the oil consumption issue. During these issues, no service engine light ever came on. The car had to be taken back to the dealership after the service engine light came on which indicated that the cam shaft actuator solenoids and catalytic converter needed to be replaced. The catalytic converter most likely failed due oil seeping into the exhaust which coated the ceramic substrate & the excessive heat experienced by the engine (as indicated by the cracked manifold) damaged the ceramic substrate. Oil consumption leads to excessive heat from the engine which can be a fire hazard. Engine stalling due to oil consumption leads to crash safety issues.