1. The adjacent state concept was done away with in 1986 by an amendment to the GCA of 1968. This is explained in the August, 2004 BATFE FFL Newsletter:
http://www.atf.gov/publications/newsletters/ffl/ffl-newsletter-2004-08.pdf
2. During the time that you work in Alabama and sleep in Alabama, you are a resident of Alabama. This is explained in 27 CFR 478.11:
http://edocket.access.gpo.gov/cfr_2003/aprqtr/27cfr478.11.htm
And on page 39 of the Federal Firearms Regulations Reference Guide:
http://www.atf.gov/publications/download/p/atf-p-5300-4.pdf
3. The problem is that you must have a government issued ID card that proves to the FFL that you are resident of Alabama in order to purchase a handgun from them (a long gun would be no problem because the adjacent state provision went away in 1986).
So, your options are:
You can purchase a handgun from another resident of Alabama in a private party transaction during the time that you work and sleep in Alabama (because ID requirements are not specified for private sales). But you would have to convince the seller that you were a temporary Alabama resident.
OR
The handgun has to go to an FFL in your home state that your driver's license or other ID is from, AND you must retrieve that handgun from that FFL in person.
OR
Some states will issue ID cards to temporary residents. It won't change your driver's license, it will be an ID card. I have a Washington ID Card and a Wyoming driver's license. The Washington ID card allows me to purchase handguns in Washington without any hassle.
It is against Federal law for an FFL from your home state to ship a handgun directly to you unless it is a firearm that is being returned to you after repair or replacement, and in that specific case it does not matter which state you are in.
BTW, in the August 2004 Newsletter to FFLs, contiguous means the same thing as adjacent.