I think your problem is still with the venting. Snakes can make a hole in the blockage without actually removing it. You might rent a power snake (one that is turned by a power drill motor) to clean the vent. I would then run a garden hose down the kitchen sink vent far enough that it pushes the blockage into the drain pipe, turn the hose on and then pull it out.

Do you mean the rooftop vent? I did clean that out with a snake last year. I took a hose up on the roof and the stack stated to fill with water. AH HA rented snake, tried water thing again and no blockage evident. Blurpling seemed to stop for while. Could be tree close to the house. IF you think it's that vent I'll put a vent/stack cap on it next time. I tried to draw a diagram here, but when previewed, it didnt turn out right so I left it out.

removed cleanout plug in basement and no blockages seen when water ran in either sink

Roof vent 3 stories up (victorian style home)
kitchen sink and bar room sink on same floor that transitions thru the floor to the basement. where it all ties into main drain going thru wall

This is probably totally off but by chance you didn't have an ac put in? When we put central in our home, they ran the drain for it into the stack for the upstairs sink and it started blurping whenever the ac ran in hot, sticky summer weather. Had it re-run into the actual draining and voila no more troubles - don't know why it was that way to start with, don't even think it's code! And yes it was properly inspected, so don't ask me.