All you figured out was how to bias the opamp when running it on a single supply. This connection will do nothing to solve the underlying problem that only a few opamps are capable of pulling their output pin nearly all the way to the same voltage as their positive supply pin is tied to. Several posters told you this, but so far you have missed it!
Go read the Voh spec on several opamp data sheets. All opamps are tested to determine the maximum voltage that they will pull their output pin to. It is usually specified as Vpos - Δ, where Δ is 2V for most opamps. In other words, regardless of how you bias an opamp, when operated off a 12V supply, it can never pull its output pin higher than about 10v!!!
There are some CMOS "rail-to-rail output" opamps which are cabable of pulling their output pin within a few mV of the postive supply PROVIDED THAT VERY LITTLE CURRENT IS BEING DRAWN FROM THEIR OUTPUT PIN. This is why you were told to raise the impedance of the feedback resistors to the fractions of megΩ.