The Bearss book has already been a great help. In a May, 1862 report on the river defenses of Vicksburg, it says that there were two initial batteries that appeared to have four guns each - one was on the hill just north of town (almost certainly Fort Hill) and the other was on a slope below the city. I was able to cross-reference this with a Confederate journal entry that describes the 8th LA HVY ART taking possession of a four-gun battery 2-3 miles below the city, soon after their arrival on May 5, cannon details given as well. I don't know which of the two was the first planted, but at least I now 'know' that they manned a battery prior to the Depot and Whig Office Batteries. I had read this bit of information on the battery below town previously, but didn't make the connection. Everything is falling in place.