From my experience with a friend that often picked up salvage vehicles and rebuilt them - your results may depend on the DMV in your state.
If you are trying to erase the history of the vehicle then you have some legal issues to wrestle with, and I don't condone it.
If you are trying to fix up a vehicle that is a financial write-off for an insurance company and breathe second-life into a vehicle that may have many more years in service while being up front about it's history, then it depends on the appetite of the buyer as well as the confidence they have in you to fix the vehicle properly.
What are your intentions thats the real question. To flip and sell? If so, stay away. I wouldnt touch a salvaged title with a 10 foot pole, and 99% of people when you inquire about the title say "theft".
To make a project vehicle for yourself to drive around and enjoy? Sure, go a head and do it -- probably do pretty well with it.
I bought mine as a salvaged titile. It was all cosmetic damage. Hard top needed fiberglass repair, fender, hood and front grill were all bent and scratched. Windshield was cracked. None of the damage kept it from being driveable. Frame was straight, drive train were in excellent shape. I feel it was a good deal and have never been sorry that I bought it.
I buy, fix, and sell cars as my side hobby (did it in AL, do it in NH); I usually do about 2-5 a year (within legal limits); and I won't touch anything salvage, it's just not worth it to me. Anything I sell, I want to "beyond reasonable doubt" know that I'm selling a good safe vehicle without a questionable background; having a salvage title means that at least SOMETHING major has occurred.
Anyways, everything these gents have been saying is right on in terms of resale. Not buying to fix and sell? Ok, but buying something for personal use with the "It's for me, I don't care about resale" outlook isn't exactly easy. You have a road ahead of you if you want to register in Alabama.
To register a rebuilt titled car, you have to have it certified by an Alabama-certified rebuilder. Can you do the rebuild? Sure. Will it be harder finding someone to sign off on it? Yes. This is because most of the certified rebuilders are the people buying these cars, rebuilding them, and selling on for a profit. The surity bonding to become one has to be paid off somehow.... and inspecting people's "home resto's" won't do it. Another problem is if you hire a rebuilder with the "Here, rebuild this and certify it" approach, they can do whatever they please to "certify" it; trust that they won't be doing the bare minimum, at the end of the project you'll have spent Rubicon money for a previously wrecked TJ.
I went through the whole recertify deal with a gorgeous, fully rebuilt (but still with GA salvage title), third gen RX-7 from GA. The thing was spotless, but the title was salvage. I lost out money on flights to inspect the car, but I was glad I didn't transport it and not have anyone to "bless" it once I got it back down to the coast. And man oh man did I try, but the "fees" to do it weren't worth the savings to me.
I wish you the best of luck, but I'm going to have to say my opinion is stay away. Maybe I'm wrong here, but I'd hate to see you get bit. Maybe someone who's still down there (I'm not anymore) knows a bit more than me and can coach you, but I wouldn't go at it (especially shipping those ones you listed) without having someone who can help with the process. Another word of caution is be VERY careful about the salvage auctions you see on sites like Copart; if you can't physically visit and inspect the vehicle, it's probably not worth the fees.
Thank you so much guys, you really helped a lot. I thought I'd drive the car for some years and then resell it but now I realize that I'll have to keep it) Jaminjer, did you buy your car at auto auction?