I wonder how many experienced admin staff are currently out OF work and claiming benefits, if offered they might be happy to take on this task on a short term contract basis. Temporary centres in large cities, clear the backlog with a corresponding reduction in benefit claimants, and keep on the best staff to bolster existing teams,
There would also potentially be a number over retirement age who wouldn't mind say 6 months work.
Probably not do able but it's another way of looking at the argument about costing.