Based on everything I read, I would suspect the timing to be retarted or an excessively lean condition. Whether that is a mechanical problem or an electrical problem is up in the air. I would suspect the later though due to you indicating it was an intermittent problem. I would start by verifying mechanical specifications on the engine because those are generally easier to deal with. Verify fuel pressure and ignition/cam timing. In the electrical department I would check out the O2 sensor, TP sensor, and possibly swap in another igniter for fun. Another issue that seems to be becoming ever more popular, though still relatively rare, is the engine wiring harness getting a defect in the injector wiring at one of the splice points where it branches off to one the two injector pairs (group fire system). This seems to be happening due to water induced corrosion and age. This problem usually manifests itself as a stutter/misfire. But, I could imagine it causing an intermittent lean condition. Anyhow, stick to the basics because that's most likely your problem. It's rarely a glorious diagnostic procedure followed by an obscure repair. If you think it is, then it's time to get some fresh eyes on the problem to start from scratch.

A little side thing I noted. How is a multi-port fuel injected engine able to continue running (dieseling) when the ignition is moved to the off position? Dieseling is certainly indicative of an engine running lean, but this is only a problem that usually plagues carbureted engines. As soon as the ignition is moved to the off position, there is no longer power to the injectors and subsequently no more fuel. Dieseling in a multi-port fuel injected engine would almost certainly indicate leaking injectors bleeding off the residual pressure.