Hi,
From your description, and the phase shift observed, your three-stage amplifier must be ac-coupled between stages. These R-C couplings will give less than 2 x 90 deg phase shift hence the 10deg lag. You may get close to 0 deg shift if you can make the capacitors much larger - how close do you need it to be?
Alternatively, for a 10 deg phase difference have you considered a phase-advance C-R circuit at the input of the amplifier? You will need to adjust the overall gain a little, to compensate for the C-R network, but it's a lot easier than using tailored feedback around the whole amplifier.
Using negative feedback in the way you suggest is possible but very complex. Without doing a Nyquist plot of the complete setup you are liable to make the whole thing unstable and turn it into an oscillator at some other frequency.