Minimum CMRR design requirement
Your calculation of the gain (assuming an ideal op-amp) is not an approximation- it is exact. 

The problem is underconstrained. Try setting R1 = R3, which, of course, means that R2 = R4, from your second line above.  

The CMRR will only enter into the tolerance calculation. You can make the tolerance of each resistor worst-case in the correct direction that it changes the gain either up or down (pick one).