By the way, if we look at what's transpired, QE hasn't decreased rates towards the long end of the yield curve. Mortgage rates have increased and housing has seen no tangible benefits in my estimation.
Since you seem to like the deep water, here goes!
QE is pretty straightforward in that monetary policy only generally affects the short end of the yield curve, i.e. the yield on short-term Treasuries (under 3 years). In 1961 and again in 2011 the Fed tried "Operation Twist" (yes, named after Chubby Checker's hit song and dance craze). The Fed bought long term Treasuries to force the price up and the yield down, using sales of short-term Treasuries acquired in the course of QE to avoid printing money. Re-evaluation of the 1961 episode lead to a conclusion that Twist had been more effective than thought at that time and that another attempt might be worthwhile.
The problem was that the amount of short-term Treasuries on the Fed balance sheet was inadequate to carry out the level of operations thought needed. So the QE/Operation Twist experiment did not meet expectations. Since there was really no downside, I'd call it a success.
Currently the Fed says that it's long term inflation goal is 2%. If credible, I think this puts a floor on the long-term Treasury rates. I think we are in the situation of states that have legalized casino gambling and a lottery. Both generate revenue, but not as much as you would expect by adding projections together. Both are tapping the same pool of money. Similarly, the more tools we deploy (at least monetary tools) to lower interest rates as a stimulus measure, the less effective the combination will be. These things are simply not additive.
IMHO the best policy is to restrict Operations Twist to availability of short-term Treasuries in the Fed portfolio. We are stuck with the yield curve that does not flatten sufficiently, but I do not see a policy that would make this better without dire side effects. The announced inflation goal is a better tool. The Treasury--TIPS spread has gone from 1.5% to 2.2% over the last half year or so. I have no statistical evidence, but my gut tells me that the markets are becoming convinced that the Fed is serious about the long-term inflation target and that is at least contributing to the rise in market inflation expectations.
Now if we could only figure out how to take those mortgage-backed agency securities the Fed has been buying up in QE and dismantle the tranches so the underlying mortgages can be resolved........