Wow, lots of feedback today. Thanks all.
TiN - you are right that the use is for business, but my questions are largely out of personal curiosity, so I guess it is partly crazy experimenting! If you come across a decent 5720 in the $10k-ish region again, let me know

I have had a pertpetual eBay search on 5720s (and 5700 EP3) for ages, but I haven't seen them cheap enough unless they have some errors. I don't have the confidence to build one up like you have done - impressive stuff.
I'm away on holidays this week (bad timing for this thread!), but I'd be happy to put some numbers up and collect more data when I get back to the lab. I don't have any sources with better stability than the 5522A, so I might not be able to give significant data on the 8588A performance, but I could collect and present some data on the 5522A stability if that would be of interest. It sounds as if RYcal is also setup well to collect this data with the same models.
Regarding 3458A vs 8588A - to be honest I was dreaming of 3458A for many years, and I understand it is still the DCV gold standard on EEVblog. However, when it finally came time when I had a budget available, the 8588A (at least by its specification) seemed better suited to my application. For example, I mostly support the process industry where 4-20 mA is an important meaurement for low uncertainty, and the 10mA range on the 8588A is ideal for this, where the 3458A would jump up to 100 mA range. If DCV was my primary focus, the 3458A would still be my pick based on the opinion in this forum and the high regard given by NMIA when I attended a course their a few years ago.
bdunhum, in the two DMM scenario I am considering the 1st DMM to be connected closest to the high terminal of the calibrator, and 2nd connected closest to the low terminal. I have tried many combinations of guarding and grounding, such internal guard on both DMMs, external guard connected to calibrator guard, and other combinations in between. The guarding does impact the comparison. I note that Fluke calibrate them with internal guard on ACI, and this does offer the closest comparison between the DMMs. From memory, the difference is perhaps .07uA at 0.1mA 50Hz, with the second meter always reading high. When I get back to the lab next week I will look at the data again across a few currents/frequencies and provide more data. It is most obvious at lower currents where the resolution makes it easy to observe. I have swapped the DMMs between the 1st and 2nd position, and confirmed it is the position in the circuit rather than the DMM. I am of the opinion that the cause is that the second DMM does actually have more current flowing across its shunt, rather than it reading in error, but I don't know why/how. Anyway, I'll probably just pack-up this experiment as time wasted, and stick with the characterisation approach does provide a excellent agreement between the DMMs.
RYcal - if you establish any short or long term stability info on the 5522A (or 8588A), I would be very interested, as would the community I'm sure!
Kleinstein, thanks for you feedback. Yes, it is early days for the 8588A. My understanding is that the 8508A was a "good" DMM, so my hope is that the 8588A will at least be a "better" DMM. Time will tell with regards to how well it transports...