Well man, I do not know what else to think about the breathing and rich condition. I just lied, a little bit! (:)

I rolled back over your initial post and you said something about it being "nothing but problems for the past three months". We may need to pick on those for additional clues.
Previous Owners and their desperate mechanic(s) may be at play here.

You changed out the AMM. I hope you have the right numbers of AMM,ECU and is working together. Could there be a problem with the connector or some sort of wiring issue? I feel there may be a communication problem and the limp mode may be doing its thing in a limited way while the AMM is talking to the ECU and so forth.

Everything adjusts very quickly which to me, adds to the hunt.

Mechanically you have gone as far as you can go.

If you unplug an AMM on a properly working engine, you can drive around but the pull off power is a dud until you get up some speed.

In this case, you have changed many parts except the in-between things.

Oh No, another warped thought from my head. I do not know what the smaller vacuum hose does with the operation of the flame trap but have you tried to disconnect the flame trap hose that feeds back to the accordion hose that fits between the throttle and the AMM?

Try plugging off that inlet hole in that hose and run the car about leaving the crankcase open to the atmosphere or to the wind, to be less technical. (:)

I am wondering if there is excessive air coming from the crankcase that is messing up the AMM job by bypassing it. Possible it is a cracked in the flame trap housing or bad o-ring. Some people have had issues with air leaks behind the AMM doing many random things! This is straw grasping, you know! (:)

You know, I started out thinking about your statement about the PO changing out the HEAD and these thoughts up above just messed with mine!

Thought I would share some of it. We all are going to slap our foreheads, when it turns out to be a simple explanation!
Phil