Your contractor's layout is preferable, though moving the lights closer to the counter tops would be fine - between 24" - 30". If you use lights like the Cree CR4 or CR6, there will be sufficient spillover to augment the light from the pendants over the island in the center of the room. If the pendants provide insufficient light, they can be swapped out/ higher output led lamps may be used. Rationale The counter tops will be better lit with UCL than cans. Even if you do have the ability to put can lights over the counter tops, the distance to the counter top reduces the amount of incident light. There should be sufficient distance from the crown molding around the upper cabinets to the cans so that the trim can be fit and look properly spaced. A more regular pattern is preferable as it isn't like a random pattern of holes in cheese. Eyeball cans are more troublesome in the long run. The final location of the cans will be determined by the layout of the ceiling joists as well as obstructions above the ceiling board. There has been ample discussion on the DIY led recessed lighting guide for kitchens thread on this topic

The wall is 50" inch long between kitchen and dining. And the sink wall is 121" inch. I have actually done a price quote for cutting the wall, most of the contractors that I spoke to tells me it's not worth it to shorten it, as it costs quite a lot without gaining much. Somewhere between 5~10k depending on how much I shorten this load-bearing wall / hide the beams or not. I have already bought the 36" fridge... so not really an option for me now. Again, I know it's compromising some functions which are (1) DW gets in the prep space, (2) not much space between range to wall? Back to lightings, any general suggestions on whether to use 4" or 6" housing? And does it make sense to do one extra on top of the sink? Also, what length UCL would you recommend?

I would do something like those with the cans centered over the edge of the counter so you have less shadows. I added one directly over the sink which may be too much...

IMO a track light with LED bulbs in daylight color so 3500- 5000k range will the br a much better choice than a pendant and give you a heck of a lot more light than you are getting from that fixture.Get some art on the wall and ditch the clock especially in a kitchen where you have clocks everywhere.Repacing the upper cabinet doors with frosted glass would make a huge difference too.