If the emitter current source is OK,the gain should depend very little on common mode voltage.
You can find out the dependence by using three voltage sources.
V0 1 0 DC 0V (Vcommon mode)
V1 2 1 AC 0.1V (V diff/2)
V2 1 3 AC 0.1V (V diff/2)
nodes 2,3 are differential amp inputs.
By sweeping V0 you can see how this affects the AC gain.
In HSPICE make and an AC analysis using the common mode voltage as sweeping parameter (go to the AC analysis section in the HSPICE manual) You can make AC analyses while changing DC bias. You'll get a family of AC results with the common mode voltage as parameter.