You're in luck - There are many ways of achieving this.
Stacking voltage references will not work - they are a means of reducing a voltage to an well defined level.
If this is a one off then buying one of the many many many products available may be easiest.
If DIYing - various boost converter iCs exist. Most of these do not have the voltage rating to handle 160 VDC directly, but use of a transformer will give you N:1 stepup.
I usually start with recommended and olde but goody smps IC MC34063. There are many better but this about anything at low ICcost.
Fig 19, page 14 does what you want. If you want REALLY low idle power there are better IC.s As you want only uA you want an IC that goes into burst mode at low load. Run a long long time on batteries if needs be.
I just noticed that they have pin 1 connected to output collector. That limits Vout to 40V. Instead return pin 1 to Vin via a resistor and Vout can be "high".
Here is a circuit that uses a more modern IC an that achieves 150-250 VDC with essentially the same core circuit as above, but with improvements. Uses Maxim MAX1771 IC. Datasheet here . Be wary of single source and availability - but seems to do your job exactly. Their design is aimed at 12V in but the IC will do 2V+. IC uses PFM to get low idle current at low load - high in your context and better can be done. If necessary a system that shuts down to essentially zero drain most of the time under uA loads can be implemented.
From here - Nixie HV Switching PSU
Note in text their comment on layout affecting efficiency. Stray capacitance and other AC losses matters at this boost ratio. Note eg lack of ground plane near inductor. Using their supplied PCB design would be wise.