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
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.