A burn in at 150 C would not help much with latice defects in silicon. The temperature is just way to low. For annealing the silicon, think about 700°C and up, so nothing to be done with the ready made part. Some of the process steps to grow a new oxide layer already works as nealing for much of the earlier damage.
If at all it may be some impurities (e.g. hydrogen) to still move inside the silicon, the silicon itself is fixed.
Surface charges can indeed by a problem, but here it would be more like having a surface that is not susceptiple to catch new one. The glow from hot electrons visible with many zeners or transistors in avalance mode is a thing to avoid, as this could also excite deap states in the oxide.
Water can bond relatively strong to the oxide surface: In vaccum it takes some 100 C to get it off in reasonable time. This water causes stress, kind of making the oxide swell. I have seen the water in/at the surface oxide bend the silicon (though with thin silicon parts). With the sealed case the water is kind of fixed and nothing to get it out or in (not sure which case is better). The water at the surface could cause some hysteresis, like a new relaxation after oven turn on after off for some time.
I would expect the burn in to be mainly about the epoxy / glue. Here there are 2 processes:
1) stress from mismatch in thermal expansion, of the glue, die and case . At the glass temperature or slightly below the relaxation should the fast enough, that there is no more stress from processes before.
2) relaxation in the structure of the amorpous polymer. Well below the glass temperature the material wants to get a denser structure, but the relaxation gets slow and the actual structure is usually less dense than the equlibrium. The degree of order in the strcuture also effects the strength and speed of the relaxation. Initially it can be fast, but once relaxed it can slow down the process quite a bit.
Chances are a good process would be cure at a high temperature, like 150 C (I don't think this would need a full week and I don't think cycling would help), than cool down relatively fast and to a relatively low temperature (maybe even room temperature) to let much of the stress relax with a still relatively soft structure. This step may take quite some time. Than heat up to a temperaure a little (e.g. 20-30 K) above the later oven temperature (but below Tg - 50K) for some time to get the structural relaxation done, without adding much new stress. The last step may well be with just the internal heater and the zener running.