I didn't quite catch you.
LTZ1000 is not operated in shunt mode(2-terminal mode? or zener diode mode) like REF5010 or LT1021, where the supply and the output are the same.
The 7.1V output of a LTZ1000 circuit comes from two sense pins which are not the same as the supply rails. Ideally there should be no current flow through these sense pins in either direction(in or out). All the 28 sense pins should be connected in series fashion in order to get a perfect 100V. If any of the 14 power supply is not floated, there would be a current flow through some of the sense pins and degrade the performance to say at least. That is also the reason why devices like REF5010 can be cascaded in the simplest way.
I was thinking on the full configuration for each one, with the output buffer which can source current. Use the output of the opamp to power the next stage, not much juice needed as the previous stage should balance the current. The problem, as usual, would be the heaters. In this config, the ground of the first stage, the pin 1 of LT1013 (or after the diode) of the second and the V+15 of the third should be tied together. Some tweak of the circuit should probably be used to manage the zener - sense terminal. I'm not saying is an easy solution but seems there may be a way, and once solved for one stage would take the need of 14 clean floating voltage supplies.
Isn't a better approach (cheaper and more reasonable) to use an amp stage to take that 7V and turn them into 100V? There are really stable resistor networks and you could ovenize them to get even better stability. A pain LT5400 can't handle 100V but can handle 60V without trouble, so two of them and keeping the LTZ in the middle would do it. To complete the circuit two low drift opamps and a few high voltage transistors would be needed.
I'd guess the REF5010 approach as a transfer and a KVD to calibrate it to an LTZ makes an easier world to live in.
JS