First of all I don't get ur point which says "can a design be done without i/p common mode range???". I get it as follows: you want to design an OPAMP without difficult conditions on the i/p common mode voltage, If this is true so u may try to use OTA folded cascode OPAMP, it has a wide range for i/p common mode levels.
Also I design before an OTA folded cascode which has a gain about 65 dB, with same supply rails. (I get this gain from a single stage)
About the point of settling time, I think it can be measured from the slew rate (I am not very sure from this point)