Unexpected Behavior with Continuous Read Mode on AD4112

I'm trying to perform a continuous read of four channels on the AD4112 as described on page 35 of the datasheet. I have channels 0, 1, 2, and 3 configured and enabled with different combinations of single ended and differential voltage mux inputs along with different filter configurations. When I perform four sequential single conversions, I get the results I expect. However, if I try to use the Continuous Read mode, it appears that the 4112 only converts channel 1 continuously. I have verified this by examining the data being returned, measuring the conversion time, and setting DATA_STAT in the INTERFACE register to append the status byte to the reading. I have also confirmed that my logic analyzer trace is identical to Figure 55.

So, I'm stumped. I was hoping to offload the collection of ADC data using a DMA channel on my uP but until this gets resolved, I have to collect it one conversion at a time using interrupts. 

Clarified mitigation.
[edited by: WallyBalls at 12:28 PM (GMT -5) on 27 Dec 2020]