Could I ask how you know so much about this, or where I can read something more detailed than the usual story that's reported? Thanks.
CDU theory of operation (starting PDF page 15): http://www.ibiblio.org/apollo/Documents/HSI-208435-003.pdf
CDU coarse module schematic: https://archive.org/stream/apertureCardBox462NARASW_images#p...
Grumman memo (from 1968!) describing the problem, and mentioning it is due to the reference switching to a 15V 800Hz source: https://www.ibiblio.org/apollo/Documents/Memo-GAEC_LMO_541_1...
Excerpt from the LM-8 Systems Handbook showing the reference voltage RR switch wiring: https://i.imgur.com/fMsQ7RI.png
Don Eyles describes the software side best in his book Sunburst and Luminary (which I highly recommend) but he also talks about it in some detail on his website: https://doneyles.com/LM/Tales.html