Sadly, I blew up my best LM399. (I'm still not quite sure why that experiment destroyed things, either.)
Of the references that survived that experiment, I took 5 with fairly similar voltages and wired them in parallel, averaging their voltages with 5ppm/C 1k resistors. To supply the reference current, I used a LT1236 and some 5ppm/C 3k resistors. I think all the support circuitry drifts are attenuated by at least 1000:1, but I used 5ppm stuff anyway
Inspired by Mickel T's super-insulated reference and the Bob Dobkin comment to keep the heater current down, I also put them in parallel thermally as shown in the attached pictures. (I've replaced that proto board with a proper PCB, but didn't take another picture before taping it all back together.) With a 30V heater supply, the combination of 5 LM399 draw about 15.5mA heater current at around 15C ambient; 3.1mA per LM399, which is a decent reduction in heater current, I think.
I monitored the setup overnight along with ambient temperature changes to get a rough feel for the relationship between heater current and ambient temperature: about 150uA per C. I then put the foam cube inside a cooler and monitored the results. At its peak, the heater current was 20.25mA and the voltage shift looked to be around -26uV; a fine result, I think, and suggests I'm getting better than the nominal 0.5ppm/C tempco.
I want to do the 7V to 10V conversion with LTC1043s, but that involves much faster rise times than I've designed for yet.