Thanks everyone for your comments/suggestions. Looks like another mod will have to fix what should never have been so complex in the first place. A simple command on the sinks to "wash dishes" would avoid all this frustration.
Thanks @greenXen for this: .... but it really doesn't explain anything and it simply isn't true. I've done testing in other builds, swapping out sinks to try and find the pattern but it baffles me every time. Unfortunately I have found that typical of EA explanations.
It's not that simple, but the short answer is that they will prefer closer objects to those that are farther away. Keep in mind that this system needs to work for all cases as we tried to make it as general and extensible as possible. The same system tells your Sims where to clean dishes as the one that tells them where to sit to eat, so the tech has a lot of masters and a lot of use-cases. We try not to special-case anything and let our design team get creative with the special-sauce like this (it is possible to add special scoring in some cases).
We will probably address this eventually but we also have a lot of other things to integrate into our system right now and we have to prioritize.