Here's something that I'm curious about. You've said the replacement engine is running great. But this does sound like a true misfire, not something that's being incorrectly posted by OBD. So is it possible there is something actually physically going on with the replacement engine, not related to the swap?

One very common thing that comes to mind is the plug wires degrading due to oil in the plug wells as a result of the VC gasket leaking. This is very common on many vehicles, and happens like clockwork on these Aveos. And even a low mileage engine would probably see this after almost 10 years. So I'll ask if you noticed any sign of oil in the plug wells? If so, you might consider replacing the wires.

But if the replacement is really as solid as you say, have you considered hanging on an '06 ECU (maybe one from a U-pull), just to see what that does?

And here's one other thought. How about trying to ask the commercial engine guys (Jasper, ...??) about an '06 engine installed into an '05. They must need to have lots of inside information about the non-matching swaps, and maybe can supply the magic piece of information you're need to know.