I'm not sure how expensive this type of sitting would be, but can you add an option to view data by month in addition to case blocks for IOE? (I'm not sure if it's possible with other receipts.) Case blocks seem to have a month that the majority of cases were filed in. They can even be filtered by the week the application was recieved since those seem to be a bit consistent as well. At that point, it becomes easier to see the receipt month of the bulk of cases that are currently being approved.
In the past few weeks they seem to be moving through a block a week. If the rate at which they're moving can be guesstimated, this gives an idea as to when to expect an approval.
The only issue I see with this feature is people tend to take these types of analysis to be absolute truth, but I think it could possibly be something worth testing out in beta.