2008 Pontiac G6 P0352 Code: Diagnosis and Fix for Poor Idle, Sluggish Acceleration, and Limp Mode

I own a 2008 Pontiac G6 base model with a 2.4L engine, currently at 141,000 miles. The vehicle is experiencing significant performance issues: a noticeable rattling noise during idle, which worsens when the climate control (heat or AC) is active. While it idles smoothly about 70% of the time, it occasionally shudders and nearly stalls. Reverse gear operates normally, but when shifting into drive and accelerating, the car feels extremely sluggish—like it's being bogged down. Shifts are rough, and I've experienced limp mode three times (displaying 'reduced engine power' message). Each time, I’ve had to shut off and restart the vehicle to temporarily reset the system. Fuel efficiency has dropped dramatically, and the car seems consistently strained. The issues began after my battery started corroding and the driver's side headlight failed due to a burned socket—though this may not be directly related, it marked a turning point where the car’s overall condition deteriorated. Around 128,000 miles on the freeway, I attempted to pass another vehicle on a hill. My RPMs spiked to 4,000 and then stalled despite my vehicle slowing down—this happened on one or two prior occasions before the Check Engine Light (CEL) illuminated. A diagnostic scan revealed codes P0011 and P0013, which I addressed by replacing both camshaft position actuators. During this time, performance worsened further. A new code appeared: P0014. I then replaced both intake and exhaust valve actuators. Afterward, the car developed a P0420 code (catalyst efficiency below threshold). There was also a reported mass air flow event—though the auto parts store refused to print out the exact code—and another code labeled P0068 (distinct from the MAF issue). Eventually, only P0420 remained. I’ve already replaced all spark plugs, thoroughly cleaned the throttle body with throttle body cleaner, and upgraded the air filter. I also noticed a small amount of oil in the intake tube (from air filter to throttle body) and on the spark plug tips—though oil changes have been performed regularly and are up to date. After two days without a CEL and an 80% improvement in performance, the Check Engine Light returned with full force. The current codes are P0420 and P0352. Despite replacing the coil pack for cylinder #2 (the second from the passenger side), there has been no improvement. My main questions: How can I resolve the P0352 code? Could I have replaced the wrong coil? The replacement was done on the second cylinder from the passenger side—could this be related to the CEL being active during an idle relearn process (which only lasted two days before the P0352 returned)? Are there any other potential causes or diagnostics I should consider?