A naive reply from a newbie:
Increasing the Zener current in an LTZ1000 would be a trade-off of worsening the long-term drift performance in order to gain lower noise performance.
If low noise is the important bit (and not long-term drift), a 2DW232 would be much cheaper and lower noise.
If you need good long term drift and lower noise, my guess would be that multiple LTZ's averaged with resistors is the only solution.
Not only is this super expensive due to the cost of multiple LTZ's, but it is worse than that: the importance of the averaging resistors (their contribution to tempco errors) is proportional to how far apart the LTZ's are in terms of voltage. So ideally, you'd have a number of LTZ's to choose from, so that you could select several which were already bunched close together in terms of Vz voltage.