OK, I have futher refined the model using additional info from the timeline threads and based on:
four May approvals and one June approval where the approval dates and ceremony invite letter dates are both disclosed (2x 14 May/7 Sep, 20 May/8 Sep, 27 May/9 Sep and 9 June/20 Sep)
indication that the Home Office stopped sending invites for approvals granted after 18 March and that they started clearing the backlog of those approvals on 7 August
I working out weekdays instead of calendar days to estimate the delays, but that did not make much difference, naturally
As you can see from the list below (which you can interpolate and/or extrapolate for any given approval date), the median expectation of the delay in printing the invitation letter drops from just over 14 weeks for 15-June approvals to 7 weeks for 29-Sep approvals.
One should another 9-20 days to this median delay to allow for postal delivery.
Median projection for the date on the ceremony invite date
Approval Dt - Invite Letter Date (add 9-20 days for delivery)
15/06/2020 - 23/09/2020
01/07/2020 - 01/10/2020
08/07/2020 - 06/10/2020
15/07/2020 - 08/10/2020
22/07/2020 - 13/10/2020
30/07/2020 - 16/10/2020
01/08/2020 - 19/10/2020
08/08/2020 - 21/10/2020
15/08/2020 - 26/10/2020
22/08/2020 - 28/10/2020
29/08/2020 - 02/11/2020
01/09/2020 - 03/11/2020
08/09/2020 - 06/11/2020
15/09/2020 - 10/11/2020
22/09/2020 - 13/11/2020
29/09/2020 - 17/11/2020