My Whirlpool-made Kenmore top-load washer is thumping in spin cycle. Changed coupler and re-leveled machine. No change. What next?

It sounds like you've done some hard work there!
When you had the cabinet removed to replace the motor coupling, did you look for missing/un-tightened bolts? Was there any debris or ground down plastic or rubber pieces anywhere under the cabinet? There are rubber vibration dumpers between pins on the motor and the mounting plate, did you check all four are in place and properly positioned? It would be important when you were putting the motor back on.
When you were leveling it, have you extended the levelers enough to exert some pressure on the floor, not just level the machine when it's idle. If back legs are self-adjustable in your model, check that none is stuck.
How springy is the floor itself? It's more important for front-loaders but top-loaders could get it shaking pretty bad sometimes, too.
I would also check if the drive block (the part that connects the drive shaft to the basket) is tightened. It requires a spanner wrench to tighten it and if someone by any chance has done some work there before you and didn't have the right tool, it may have become lose. It might have been lose all along as a manufacturing defect, too. If you remove the agitator and  have access to the drive shaft and the gearbox below, see if any part has some extra play to it or not tightened in its mount or a clip came off, things of that sort.  if you are very sure you've eliminated any possibility it's not leveled, and since you've already replaced the motor coupler, you next step from there would be to go down to the transmission anyway, so start at the drive block and go down checking for lose or worn out parts along the way.  
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