Codes P0300, P0301, P0302, P0303, P261B, P3190

What's the mileage on it? Has the entire EGR path been cleared, or at least checked?
Could the noise "between the ICE and the transaxle" be the damper coupling between engine and transaxle? They infamously rattle when a cylinder is misfiring.

 

This is the clanking sound my car was making when number two was going south and taking on coolant enough to make the engine stumble on transition and that clank would happen and then it would smooth out and then it would do it again so be looking at that number two plug or the number one apparently it's usually a number two but whatever you have to do check them all looking for water droplets even microscopic ones you might need a magnifying glass but it sounds like it's a happening.

 

A noisy inverter or EGR cooler would be very unusual, as far as I know..

 

The P261B does indicate the water pump is turning less than 900 RPM when it should be turning more, so that is something that should be investigated and dealt with.

The flow has to be reduced a lot before P0401 is set. If you look over at the EGR flow monitor results thread, we're usually seeing around 20 to 22 kPa from freshly cleaned systems. The "min" test threshold where P0401 is triggered is slightly less than 1 kPa!

Under what conditions do the misfires mostly occur? If it's at mid-loads, where EGR is in use, they could indicate clogging of the four EGR passages in the intake manifold. The monitor test only sees overall flow, so if some of those passages are more clogged than others, you can have overall flow that passes the test with flying colors, but really some cylinders get too much exhaust and some too little, therefore misfiring.

But that'll have a definite pattern, misfiring at mid-loads where EGR is used, not so much at idle or heavy loads, where it isn't. If the pattern is different, the problem is likely something else.

A good misfire diagnosis article starts on page 15 of this issue of Toyota Tech.