Yes you should use the 6th at 12 am. Thats what I have done when arriving that late.
You should be fine with Alamo they are 24/7, and the kiosks are very convenient and easy to use.
If on-line check in is available for your reservation, (it is not usually available for certain type of reservations) by all means use it, you can then just go directly to the garage and pick out a car, and your on your way.