David,
Titles Unlimited is the way to go!! I did it about two years ago & it works like a charm! However, don't jump the gun on using them, because your car NEEDS to be finished and ready to license because once you get the paperwork back from Richard Weaver in Alabama, you only have 30 days for delivery. Also, you should get insurance prior to applying with T.U., because If you have proof of insurance and a few additional $ (I think it ia about $15) you can get an Alabama license plate with your bill of sale. Also, you can get a Texas license plate(unissued year specific- ie 1965, 1966) from Larry Machacek in Porter, Texas and a year specific inspection sticker @ (281) 429-2505.
Get the car finished & call T.U. 1-800-325-8136 and follow his lead exactly to get it done.
Good luck,
John R.