Apologies for so many edits. On my phone, switching to desktop mode to upload photos. Switching back to mobile mode made me edit the post and removed all photos I added. It took me a few edits to figure this out. I'll get the hang of this quirk.

You only want the sink lighted up more?

The recessed lights should be making a 'U' shape - one linear row starting near the cabinet end at the GreatRm, then turning along the ref/pantry wall, then turning along the slider. If you need more task light at the island, change the island pendants.

I do want the island lit up more on the left side. The side facing the cooktop is well lit until you get to the sink where the light drops off. I think if I install all four lights the entire area will be lit up (double pantry and island). But we can choose to just have pendants while we eat.
Accessing the double pantry right now feels darker.

I made some measurements and will confirm with my electrician if it's possible to install another six lights with the same spacing as the existing six lights. So they will form an L shape of lights around the island. The lights provide so much light and overlapping light it will make it easier for us to use the island for task work in the future (filling meat dumplings/pot stickers, rolling and cutting pasta, etc). Thanks for the input. I'll post pictures in the kitchen before/after forum after this is done and we get everything cleaned up.

Just be aware that the lighting you have now, with the 2nd row of the tightly spaced grid, looks to be lighting up the floor mostly. Here you can see the throw: the yellow is on the counter (it is very pronounced what the can is lighting on the island), and the green is the floor. I would imagine you'd prefer most of the light on the counters and into the cabinets, so the locations of new lights should be placed for that, not the floor. Also keep in mind guessing 90% of electricians do not understand lighting, they just wire them. And you may not get uniform spacing because of joist locations and ductwork.

If you want to light the pantry interiors as well as the island surface, it looks to me that you may need to stagger the lights. That is, not 2 matching rows and not necessarily the same spacing as the current lights..

The current light closest to the fridge (in front of the cabinet to the right of the fridge) is not optimally placed, for example. Better if it were at the center of that cabinet.

Again, remember that ceiling lights do not need to be symmetrical or even - they have a job to do, and if they don't do it well, that is more noticeable than symmetry (like, who looks at the ceiling day to day?)