@Klienstein,
Oh really, you think you know more about the subject than Jim Williams, perhaps you should get in touch with Linear Tech and let them know there is a replacement available for Jim. I do not intend any insult here but it is obvious that some here do not grasp the underlying design principals involved in trying to measure very low noise levels accurately.....note that word - accurately, not in the ball park measurements.
Seriously, Jim did it that way because that was the correct way to do it at the time, moving on a few years, yes, you might be able to sub a few of the components, such as a polypropylene capacitor for that tantalum and maybe some other minor changes but the circuit as done cannot be significantly improved on nor can you duplicate it with cheaper, lower quality parts. This is not the jelly bean project some seem to think it is.
Again, you cannot measure a Gaussian noise source with an integrating or sampling ADC (that includes DVMs), it is not accurate, it does not repeat, it does not measure peak-to-peak nor RMS but will give you a sort of kind of average variable of the noise. Unless you are using a very long period of measurement, tens of seconds at least, the average of a DC-10Hz noise band will not be accurate in any way, shape or form and in the case of a voltage reference, you need to know the noise characteristics accurately and that includes peak to peak as well as RMS, average is of little use. Noise is the limiting factor in a reference, not just drift.
Pardon me if I sound a bit terse.