I've found some more info on this in Friedman's US Amphibious Ships and Craft - An Illustrated Design History.
Apparently it was proposed some time prior to 1981, when a study called AMFIST included it among the studied options for solving fire support during an amphibious invasion (the cases studied being an invasion of Jutland against a Soviet motorized rifle division, North Korea without Soviet intervention, and Southwest Asia.
In the study, they looked at a 155 mm Vertically Loaded Gun (included because it could potentially fire Copperhead or bomblet shells developed for the Army), an 8-inch/36 NUGM by White Oak (it refers back to an earlier chapter for a description, will have to dig to see if I can find it), and a Vought 9-inch rocket that could be loaded in an ASROC launcher. Also looked at were Tomahawk, a bomblet-carrying rocket missile, and Martin Marietta's Beachcomber (which was based on a Patriot missile body and originally developed for the Army's Assault Breaker program.
The 155 mm gun was envisioned as being able to not only fire the obvious Army shells, but also do stuff like launch sonobuoys, hydrostatically fused shells (i.e. depth charges), but due to the loading method they were looking at 10 rpm. The range was expected to be 42 km for guided shells (as opposed to 30 for the guided 5-inch shell), and 27 km for unguided shells.
The idea was formally rejected in December of 1983 on the basis of the gun adding 130 million dollars in life cycle cost to a ship so equipped with no real benefit over a guided 5-inch shell. (which then failed to materialize, multiple times.)
