I reconciled the current statement, then went back to trying to debug that statement. I tried to find an unreconciled transaction that made it work out, but to no avail. I finally gave up and recorded an adjustment (the first time I've had to do so in five years of using Quicken).
On this statement, there was a discrepancy in the opening balance, which perplexed me. I corrected it and went on to reconcile the statement.
After all the transactions were reconciled, Quicken told me that there was a discrepancy of $80.27 in the opening balance for the statement. I searched through the register for an $80.27 transaction to find out what was happening.
I discovered a (real) transaction from July for that amount that was marked 'Reconciled', and I discovered that the balance correction I had entered for that statement was for the same amount.
I followed a hunch. I allowed Quicken to record an $80.27 adjustment for this statement, then I cleared the Reconciled status of all three $80.27 transactions, and re-reconciled.
Sure enough, when I included the real transaction as reconciled for the statement that had had the discrepancy, it cleared up everything, and I was able to correct the problems with later statements by cleaning out the correction factors.
I suppose that what happened was that at some point I 'unreconciled' the real transaction, and just flipped it back to identify it as reconciled, without identifying it as reconciled for the particular statement it belonged to. But since it was marked as reconciled, it didn't show up as an option to be added to that statement.
I guess the moral here is that when Quicken warns you about changing the reconciled status of a transaction, there are non-obvious implications to what you're doing.
I feel pleased about sorting this discrepancy out.