As it happens I have not used the Edinburgh one but have used many times the Manchester service.
They are very flexible and pick up times are not set in stone - they ask me what time I wish to be picked up. It is interesting to talk with the drivers and they will tell stories of those who cut it to the last minute or leave them hanging around for ages
You know how long it takes from your house to the airport so either arrange direct with Etihad or get the contact details of the company they use