There's really nothing you can do to make the reference surpass its specifications (except maybe oven controlling it, but that's pretty extreme). If you need better performance than the datasheet advertises, pick a better part.
Capacitors are nice, but their values varying shouldn't have an affect on the reference output, so long as there's enough capacitance to keep things stable. But piezo effects are definitely a valid concern which must be kept in mind, especially if your circuit will experience vibration or shock. Remember that such vibration can be generated by the circuit itself if there's any high power switching going on (buzzing inductors, etc). If you use ceramic caps, stick to class 1 dielectrics, or use leaded components. Or use tantalum caps instead.