Over the weekend some efforts were made to reduce the error of the LTC1043 divider. I reduce the error, but I was at least able to characterize it. Addressing some of the suggestions earlier, I did a couple different things-
Power supply is a linear supply, Siglent SPD330X
Other sources of switching noise could be LED lights as Andreas suggested, which I have. For measurements all lights were turned off.
One of those clamp on ferrites was put over the wire harness to the board(ps leads and dmm leads)
An RC filter was added on the input to the LT1001
None of these things helped unfortunately.
Next the objective was to characterize the error at different input voltages. Here is the data:

The error seems to be approximately linear proportional to the input voltage. Would it be a valid assumption to assume an EMI induced error would be approximately constant across input voltages?
The error rising along with input voltage seems to suggest some type of leakage, not sure where though. The board was cleaned thoroughly with IPA after soldering. Also interesting is the positive offset at around 1.25V. Would that be internal leakage in the 1043? Or would that suggest the source voltage of the leakage path is somewhere between 1.25 and 2.5V?
Here's another idea, assuming the error IS linear with input voltage, would it be acceptable to add a very small amount of gain in the output opamp to account for the error? Or is this something that is better done in software?
I rather like Davids idea of using the other half of the LTC1043 in opposite phase to the currently used divider, so there's only a very small off time. I'm going to try this next.
Cheers