I did some checking and heard that the place in Memphis is no longer in business. I found their contact information so it might be worth a try to contact them.
Redi Strip of Memphis
8515 Aaron Ln
There is also a Redi Strip in Jackson, MS:
Redi-Strip Of Jackson
750 Boling St Ste C
There is another place outside of Jackson, MS that does caustic dipping and e-coating. In my opinion, you would definitely need the e-coating after having the car dipped.
Systems Electro Coating, LLC
253 Old Jackson Road
Here is their website. There is a photo of an antique car body that they dipped and e-coated, and they also mention that they cater to antique car restorers. I called them to get price estimates, but I had to leave my number on a voice mail and I haven't received a call back yet.
"You're almost as big as you say you are." -obsidianspider
Just want to put my two cents in here. This 65 fastback was dipped and after a year or so the acid, for whatever reason, began seeping out of the corners and ate the paint. This one has sat for over five years now but I have had several guys tell me that the chemicals can leech out long after you have done everything you can to get them out. Just be careful, this could have screwed up a nice paint job.
Also remember, dipping take out stuff you can't get to and replace. The boneheads here actually drilled a hole in the roof and quarters to allow the air bubbles to escape - which had to be welded back up! Unbelievable.
the redi strip in jackson ms did my former employee s 66 coupe,dipped and no problems of any sort afterwards with chemical leaching out or whatever. he did a complete show car restoration and 10 years later metal; was still perfect ect. wes