said by Dennis:
The long run between the access point in the basement and the vertical drop is what I've talked about replacing. Only problem is that if the clog is indeed between the access point and the kitchen sink I'm back to square one.
You did take apart the trap and look at it carefully? Its just compression fitting so no PVC work is involved. The trap can wind up with high density dirt/grit/metal shavings/sand, that will never wash out of the trap through gravity/poured water. No matter how much water you pour, the dirt will be picked up 1/2 an inch then sink through the water flow back to the bottom of the trap. A snake will never get this grit out.