If you had a spare ecm to switch over, you could confirm whether it's the problem. That or the injector harness - I haven't had one go bad, but I've diagnosed a couple on other cars that have gone bad.
You can try to isolate the problem by unplugging injector connectors as the engine is running. When you get to the one that makes no difference, then you know that's the cylinder that's the problem (if it is an injector issue).
I don't know "exactly" what happens when an ecm driver burns out, but I would suspect a miss in the engine that is 100% constant at all times. Maybe someone with a burned ECM can chime in.