Redstone Booster Recovery 2
The method for retrieving the floating booster was to have swimmers safe the booster and attach lines for towing by one of the landing ship's LCPV (Landing Craft Personnel, Vehicle). At this point, the LCPV is probably towing the booster behind it or in a "hip" position like how the SRB boosters were typically towed.
Here you can see that the letters "FS" have been painted on the LCPV, a common practice to identify the "mother ship" the craft went with. There is only one plausible Thomaston class ship which could be abbreviated "FS"—the USS Fort Snelling. Other records indicate it was stationed at Norfolk at the time of the trials, which were conducted 50mi offshore. Even looking at the Ashland and Casa Grande class, there is no other LSD which can be abbreviated, neatly, to FS.