I hope you get to the bottom of this as it must be upsetting for you.
With my 2, I can't handle Billy and Echo just wants chased so I pop their favourite treat in and a couple of boxes or shredding toys as this is their favourite activity and 9 times out of 10 they go straight in and are so busy and occupied they don't mind the door being closed. On those other odd ocassions I get Hughie to put Billy in and I tempt Echo to fly to me for a peanut and pop him in.
Good luck - they are so clever, sometimes too clever lol