After a frustrating hour, I discovered that the pinout for the DCK package in the TLV6001 datasheet is not correct: OUT, -IN and +IN are mixed up. It should match the DCK pinout of amps such as the TLV314. Also, the Name and Description columns don't match for the two inputs: Non-Inverting and Inverting are swapped. Last, I spot-checked another one of the "New" opamps (don't recall which one) and I see similarly-suspicious things, so another pass through those datasheets would be a good idea to save other engineers time, PCB rework and revision.
Regards,
Scott