LTC6903/6904 significant error in frequency output

I'm evaluating the LTC6903/6904 parts for a timing project and they are not responding as the datasheet claims they will. As a very simple example, I set OCT and DAC to 0 and activate CLK and ~CLK~ by setting CNF to 0b00. That is, I am writing 0 to all registers of the part. This should give me a frequency output of 1039 Hz, as claimed by the datasheet and verified by the equations on page 8.

However, the result is a 1064 Hz output. This is true with both the 6903 and 6904 parts. The errors are showing up no matter what frequency I request, there is always some error. For example, writing OCT=0 and DAC=48 (0b0000110000) should give me 1064 Hz. Instead, I get 1092 Hz. Requesting 1177 Hz gets me 1202 Hz. Requesting 2354 gets me 2407.

This seems to be a consistent factor of about 2.2%, which is well above the datasheet's claimed 1.1%.

I can provide oscilloscope and logic analyzer outputs if requested to verify I am writing the registers correctly.

If this part cannot accurately give me the requested frequencies at 1 Hz resolution in the 1-2 kHz range, can you recommend a part that will?