The exact wording that finally got a breakdown of my arrears out of the CMS

My balance jumped by about £1,800 overnight with no explanation. Three phone calls got me three different explanations, none of which matched the letters I already had.

What eventually worked was writing rather than calling, and asking for specific documents rather than for "an explanation". This is roughly what I sent:

I am requesting a full transaction history for this case covering [dates], showing each assessment applied with its effective date, the gross income figure used and the tax year it was drawn from, every payment received with the date it was allocated, and the calculation by which the current arrears balance has been reached.

That produced an actual schedule, and the schedule produced the error. A period had been assessed twice at two different rates and both assessments had been left sitting on the account.

Two things I did not know beforehand and wish I had. You can ask which tax year's HMRC figure was used, which matters a great deal if your income changed significantly between then and now. And if the CMS has made an error you can complain and then escalate to the Independent Case Examiner, but only within six months of their final response, so put that date in your diary the day the letter arrives.