change "Date Closed" on a case

We have several cases that have an incorrect "Date Closed" value, in some cases they were actually dealt with almost a year ago but.... well, it's a long story, but they sat un-closed in error.  For performance reporting accuracy we want to correct this date and have it reflect the true closure date but the field is readonly.

I check the usual workaround (mass update, CSV import, script) and none of them will allow me to change the value.

I suspect that it's looking at the system notes for the Status change date.  I still thought I'd ask here to see if anyone knows a way to change this field.