Well out of curiousity, on my way to work earlier this afternoon, I checked my own block learn and integrator counts to compare to the info you gave. They were both the same at all times, not differing bank to bank. The block learn values were slightly above 128, in the low 130's but I wonder if this is due to the fact that I'm using a set of Ford 19# injectors...
ANYWAY, on to your problem Sevillian, something occured to me while I was chugging away at work (I think about anything and everything at my physically active, but mind-numbing job). This might not be your problem, but is one of the only theories I can attempt to help you with.
The lower integrator values you are stating don't necessarily say if the car is running rich or not. Only the O2 sensors can tell you that and a O2 code would be tripped if that was the case. A cars fuel management is always trying to achieve the correct stoichiometric ratio, right? That's what your car is doing by adjusting the values per bank. Your car isn't running rich right now. If it was, you'd have major driveability symptoms that, from what I understand, you really aren't getting. It's running "correctly", as in the air/fuel mixture is correct, but it's using more fuel to achieve that.
So what does that mean?
Well, the integrator is calculated from the engine management gadgets you listed, with large emphasis on the MAP and O2 sensors. The MAP is a global measurement while the O2's are per bank. What this tells us is that the O2 on the effected bank is detecting a lean condition, and the computer is adjusting the integrator accordingly to compensate.
How is there a lean condition on one bank?
VACUUM LEAK!!! My money is on an intake gasket leaking vacuum on whatever bank has the low integrator counts.
One thing I'm curious about is to what it takes to set a E046 code, because you'd think something like this would set that. Perhaps the banks don't differ enough yet to set it?
If I remember correctly, you have an FSM (I never got one yet otherwise I'd do this homework for you as I'm interested in this). Does it have diagnostic charts for the E046? If so, take a look to see what it uses trip this. Does it use integrator values? Then follow the chart and see if it leads you to an intake gasket leak diagnosis. If so, I'd consider that to the true confirmation that this is the problem.