2003 Ford Escape P0205, P0305, P0310 and VIN Mismatch: Fuel Injector Damage or Dirty Gas Tank?

I'm seeking help with a 2003 Ford Escape 3.0L V6 that has been experiencing persistent engine issues despite multiple repairs. The vehicle was purchased in 2014 from a major Ford dealership in Los Angeles with approximately 72,000 miles on the odometer. About two years ago, while backing out of my driveway and shifting into drive, I experienced a backfire that startled me. After driving about a mile to a gas station, I noticed dirt inside the fuel tank—something I initially dismissed. The car then began stalling and the check engine light illuminated during freeway driving. I pulled over and drove home, which triggered further concern. After six months of inactivity, I used an OBD2 scanner and found persistent fault codes: P0205 (Fuel Injector 5 Circuit Malfunction), P0305 (Misfire Detected - Cylinder 5), and P0316 (Failed to Start or Run Smoothly at Startup). I replaced the front three spark plugs and coils (cylinders 4, 5, and 6) in hopes of resolving the misfires. After starting the car and driving for about 10 miles, the check engine light reappeared, and the same codes returned. The vehicle is driven infrequently—only 2 to 5 miles per week for errands, with occasional trips up to 30 miles. It runs fine under normal conditions but occasionally vibrates at around 50 mph; this issue resolves when I slightly increase throttle pressure. Freeway driving at 70 mph has been smooth. Today, I needed a smog certification to renew my registration and was told the vehicle fails due to a mismatched VIN between the Powertrain Control Module (PCM) and the actual car VIN. The smog technician stated that California now prohibits smog shops from overriding VINs to prevent fraud. However, I never replaced the PCM—this was a used vehicle purchased in 2014—and previously passed smog inspections. I visited the original dealership (Galpin Ford) where I bought the car. They confirmed that only one correct VIN exists on their records and stated that my PCM must have been altered. When asked if they could flash the PCM to match the correct VIN, they said it is hard-coded and cannot be reprogrammed. They also advised returning to the smog shop, which claims they can override the VIN in their system—despite previously stating they couldn’t. I am now confused: who is lying? I have two main concerns: 1. Is a mismatched PCM VIN a common issue when buying used vehicles? Do dealerships verify that the PCM matches the vehicle’s VIN before resale? 2. Could the backfire from 2 years ago have damaged fuel injector #5, leading to persistent P0205 and P0305 codes? I’ve tried several injector cleaners with no noticeable improvement. I recently replaced the fuel filter (which was clogged), but this did not resolve the issue. Despite no visible smoke or unusual odors, I suspect long-term misfiring may have damaged all three catalytic converters. However, I cannot confirm this due to lack of emissions testing. I’m now at a loss—how can I legally register my vehicle if it won’t pass smog? And could the dirt in the fuel tank (from 2 years ago) be contributing to these issues? Any insights or expert advice would be greatly appreciated. Thanks for reading.