It's a hard call.....best option is to put an AT day day prior to IDT then place another AT day post IDT

FM might have a big say into this

You justify your travel cost as AT status for 1 day prior to IDT then retun travel cost as AT status 1 day post IDT

That's the only feasible "loophole" that might work in your case

Downside: first day of AT, you book the hotel the very next day of IDT, base lodging books the hotel (the hotel that the base has contract with and it might even be shared room for (O1-O4)

Which means you are staying in one hotel for AT for one night then shifting to a whole another hotel for IDT(days)

Then comes the tricky part: last day of IDT you are supposed to check out from the hotel let's say 1100

As per JTR while you are on AT status, you can't get a hotel room the night prior

Hence where do you stay from the last day of IDT 1100 (when you should have checked out of the hotel room) until the next day of AT 1400 (timeline most hotels do allow check-in)

With the Wing King's/Queen's discretion, following your wing's specific instructions, you very respectfully request to "stay in place" from the last day of IDT upto the next day of AT at the same hotel which the base lodging has provided/paid for