First of all, you need to figure out why there's a drop in the flooring. Sometimes it's just minor settling, and sometimes it's the symptom of a much larger problem.

Second, flooring always comes before cabinets. Or else the cabinets go on top of plywood that's the same thickness as the flooring. Otherwise you have clearance issues with appliances.

Third, all cabinet installs begin with the identification of the high spot in the floor and all measurments for everything else start there. Find that high spot, and then you shim everything else to be level to it. You won't use standard toe kick when you have that much slope. You'll get a tall skin and rip it to size after you figure out what size it needs to be.

In addition, the other issue that could arise is if you are doing a continuous backsplash. With the counter tops being different elevations, you'd have to take that into consideration if your backsplash has a pattern.

If I may add to all the good points above check the level of the ceiling. Sad when the floor issues have been addressed and you find bulkheads built before cabs go up or crown molding becomes a nightmare.

Never a good idea to reset the height. Just shim the cabinets, 3/8ths inch is not that much. Drop the kick plate to the floor, I doubt you will see the top of the kick plate but if you do add a small trim piece there

Did a kitchen in an old house with an unlevel floor once where the cabinets were Crown Point with decorative legs mounted. So there could be no shimming; all had to be scribed. Some of the feet were brass-capped. Ugh.
Casey

If I may add to all the good points above check the level of the ceiling.

Unless you're levelling everything in an old house, you might be better off leaving off perfection. I once built a bulkhead perfectly square and plumb over cabinetry yet to come. Trouble was, since the ceiling wasn't level, my bulkhead looked slightly off.

Having "composed" in this field of endeavor for several centuries, (7 days older than dirt & thats 3 days older than baseball), I level the base from the high point, measure down from the ceiling on the low side the height of the uppers, to establish the distance between the base and uppers.
Now, you can be satisfied with a dimension less than the standard of 18" or you can trim the top of the uppers which even in modular, (bag-n-box), there is about 1/2" of material above the top.

One last thought, particular and peculiar, both began with "pee."

I have had to deal with this a time or two. What I have done was to order the same thickness material as the toe kick is which is normally(1/4") thick. Perhaps your cabinet manufacturer offers a panel similar to one that might be used on the back of a peninsula or the side of an utility cabinet. Cut whatever heights you need out of that and make custom height toe kick coverings. Hope this helps...
www.new-look-kitchen.com

This post was edited by jhodg13 on Fri, Dec 21, 12 at 12:07