Tell your contractor he's full of it bull pucky. Take some pictures and post what you mean. There is no way an island should be 39" unless you explicitly had them built higher.

1)uneven floors &

Why didn't he do his job and even out the floors before adding the cabinets and how uneven were the floors?

2)3" quartz countertop - which has a lip to give the appearance of 3".

The lip goes on the side of the counter so it shouldn't build up anything.

Measure the actual height of the cabinets. There is no, I repeat, no reason this should happen. They made custom cabinets too tall. If they bought ready made cabinets, they bought a nonstandard size. They need to fix this at no cost to you.