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I don't think that higher op amp gain can improve the psr. As I see, the following idea is can improve the psr.
1. Take advantage a pre-regulator inner power for the bandgap.
2. use the cascode current mirror.
3.refine the op amp's design. Set proper DC gain and make sure the compensation is ok. Generally, 60dB gain is ok.If the gain is too high, it is difficult to compense the OP AMP for enough PM.
4.connect a output capacitor can do it.
Depend on your bandgap's structure ,complex and the SPEC parameters, you can choose ideas to improve it PSR.
For low frequency PSRR (DC PSRR), it is about A*R1/R2. Here A is DC gain of the opamp. Usually, R2 is less than R1 for temperature compensation. So the structure is not for high PSRR. However, increasing A will still help to increase PSRR(DC). In the other hand, high DC gain for the opamp is difficult to be stable. For high frequency PSRR, it is more complicate that depends on your compensation network. The compensation will decrease high frequency PSRR because it will degrade the gain.
In my experience, the opamp BW does not degrade PSR over freq, it is actually the PMOS current mirrors and ultimately the bipolar core itself. So, in the end, to have good PSR over freq I had to add big decoupling caps :-(