Curious which test freq does your 590 have? 100KHz or 1MHz or both?
Which freq do you use?
For the calibration capacitor topic, do you have the 5907 standard caps? Or supplying your own caps?
Are you connected through the switch when doing the cable compensation with the standard caps?
You should be if you want the method to correct for it.
You mention an unwanted offset of up to 20pF when connected through a switch. Have you tried the zero method from section 3.10?
Your 590 is likely to be quite old. When was last time it was calibrated?
How are you determining the value of the reference caps?
In general, I’d try evaluating just the 590 with minimal cabling to the standard caps. If successful, then start adding in the other aspects such as the switch, etc.