When the Fluke representatives and their 8588DMM expert made a visit to our lab, they confirmed that the 8588 cannot replace a null meter like we've been led to believe. They have no answer when we asked them how to use that 8588 to balance this 752 divider. That was 1 year ago; I haven't heard any successful follow up since.
So I set up and tried some nulling with mixed results. I'm using a Fluke 8505A DMM and two 10V standards and no super-special leads in a relatively calm room, but not a temp controlled lab. I haven't used the meter in some time so I was interested to see how well the zero offset and bias currents have held up, and the answer is pretty good, with the zero at +/- 1 count (100nV) and the bias current at ~-5pA after 4 hour warmup. I then measured each standard and got 10.000018 and 10.000024V respectively, with some 5 counts or so maximum noise, but generally pretty calm and within a 2-3 counts in the short term. The meter and one of the standards do have noticeable tempco so they do drift around a bit more than that over the medium term, but I'm more looking at your issue of not being able to get a stable enough measurement.
I then set the two standards up to null them at the meter with a short between their negative sides. I didn't use any shunt across the inputs and I used the meters F2 filter and averaging. The result was a reading of about 6µV as expected, fairly calm in the short term but drifting around +/- 5-10 counts (0.5-1µV) or so in the medium term (say 5 minutes). This would be completely workable for nulling my standards as 1µV is 0.1ppm and that is 10-20X as good as even the most optimistic expectation for these standards (Fluke 731B and the 10V 24ppm model from
thevoltagestandard.com. Then I tried to sort of simulate your high-impedance source by putting an 82K resistor between the negative sides of the voltage sources and a 6.8nF capacitor across the inputs. Short term again was calm, the medium term was a little noiser, perhaps 8-12 counts. Then I used the same 1M/2.2nF shunt that I use for setting bias current, and the result was about the same reading and even calmer, back to 5-10 counts. So a high-impedance source isn't really a problem.
As a nulling instrument for things at my level, the DMM is OK albeit quite inconvenient. I can probably null two standards more accurately than I can transfer them directly with the ratio function or by just manually switching them. And by the specs of the 752A (once you get past the obvious errors in the online version) what I'm doing would be almost good enough, so presumably with the newer meter and a controlled laboratory you should be able to improve on this. Settling times are quite long and any disturbance at all will send things wildly off--such as the cat walking in, the front door of the house opening, etc. But all-in-all, the errors and instability that I observed with the nulling process don't seem to be any greater than those observed with any other sensitive measurement.
So, I'd ask--how much noise do you actually see when you try to do this? Can you make similar measurements at those levels with significantly less noise? With your assortment of equipment, I can't imagine Fluke wouldn't respond to your inquiry--ask them how they do it in their lab. The 752A is a current product, it would be amusing if they had some decades-old null meter doing this job during production.