I know this isn't what you want to hear, but I'd move the table or lower the ceiling. Somehow the idea of a 16 foot ceiling in a kitchen seems impractical to me. For one thing, it's just wasted space that you still have to heat and cool. Who or what is 16 feet tall? And I don't know about your kitchen ceiling, but mine needs pretty frequent cleaning. Scrubbing 16 feet up just doesn't appeal to me. But I guess if you can afford a house like that, you can afford to hire people to clean it. ;-)

and while you're here :) ....what type of lighting to you think looks best over a round pedestal table like pictured? The type of lighting pictured, a round drum pendant, or other?

i just had the same problem, with similar pendants as yours. If you look at my profile, I think you can see what we went with as well as others suggestions. I would say go larger and hang them higher than then your sightline. That made a huge difference for us.

The type of lighting that is typically on its own switch includes pendant lights and over sink lights. This allows for more control over the lighting in specific areas of the kitchen. In terms of combining lights, you can consider combining the under cabinet lighting with the pot lights to provide overall ambient lighting in the kitchen. The pendant lights over the seated counter can be combined with the over sink light to create a focused task lighting area for food preparation or other activities at the counter. For the room size of 10'x16', having 6 pot lights should provide adequate lighting coverage. For outlet locations, it is recommended to have outlets installed along the countertops for convenient use of small appliances. Additionally, consider adding outlets near the seated counter for charging devices or using small appliances while seated. Be sure to follow local electrical codes and regulations when determining outlet locations.