Codes P0135, P0155 and P1000?

My car listed above is a base model convertible. This car is still all stock. No mods and no tunes. (As far as we know.) I just acquired this and am trying to get it to pass the emissions test. I am not new to mechanics by any means. That being said. I replaced all o² sensors up and downstream. (Yes, aftermarket NTK's) We cleared codes and ran a drive cycle. No engine lights. Shut the car off, start again, then boom within five minutes of idling the engine light turned on with the same codes. So, I pulled up data stream on my OBDII reader and checked all systems. Noticed a FPDM Open loop. So, I replaced it. Cleared codes and ran the drive cycle. Better ignition and smoother idle! But shut the car off and back on, the engine light was back. I went over this car with a multimeter, and I have found no issues in the results. I did a hard reset on the computer and ran the relearning process. Still same codes. I cannot understand what I am missing. Thank you for your time and knowledge!