Thanks for the update.
Are the data valid timings in Table 1. TIMING REQUIREMENTS: 3-Wire Operation going to change?
Specifically:
th-CK-DO SCLK falling edge to current data invalid 3 ns min
td-CK-DO SCLK falling edge to next data valid delay 13.4 ns max
td-CNV-DO Enable time: CONVST low to MSB valid 12.3 ns max
These can make it difficult to know what data you are clocking if you are using the maximum SCLK frequency. The maximum delay is almost equal to the clock period meaning that unlike the data sheet claim the data is not necessarily valid on the rising edge of the next clock. It appears that you have to use the falling edge of SCLK and the 3ns minimum data valid after falling edge of SCLK is enough.