Your diagram is correct EXCEPT that there are no direct vents on either the KS, BT, or BS. There is only one vent for everything in the house and that is the one connected to the WC drain which is shown in my 2'nd pic in my question. Or to put it another way, every other drain in the house is "wet vented" via that one and only vent. This actually does not work. Hence my speculations about how to improve it.

I may have this wrong, but my understanding is that the vent goes on the other side of the trap than the side the drain/overflow port is connected to. The intent being to prevent sucking out the water in the trap. No? (Apologies for the late response. My attention wandered.)

I am not sure I understand what you're suggesting. The problems I am trying to avoid is having a horizontal run of vent pipe below the flood level of tub. I wonder what would be the "proper" way to do that according to "code". FWIW, I don't much care which code it would satisfy at this point. I'm trying to get it straight in my head how to move forward with this.

It's possible that providing more context might help to suggest an answer. What else is next to or near this thingee in the kitchen? Do you have any way to get an idea of what connections there are/were behind the wall and/or where they lead to?

One of the suggestions is to use an AAV (Air Admittance Valve). I was definitely considering this originally, but I had assumed that even an AAV should be at least 6" above the sink, but if it can sit underneath the sink then going that way would be a lot simpler.

Thanks! Hadn't thought about that. I'll have to look through it to see if there is a fit to my wacko situation. FWIW and possible future reference, here's a link to a google images search venting island sinks. Appears there maybe be a number of different possibilities to consider.

About venting. Partly I'm thinking long & hard about this before actually doing anything because I see NO way to vent the kitchen sink "to code". The sink is underneath windows jutting out in a rectangular bay (?) about 4' deep by 9 1/2' across. The vent pipe is not supposed to go horizontal until it is > 6" above the sink/counter. I don't see any way to do that except putting a vent pipe in the middle of kitchen floor or counter. I suspect this is part of why it has never been vented. If I can figure out how to phrase it, I may ask this as a separate question.