Neil;
You probably know most of this. Several houses were used as hospitals in the area. See this article:

http://battleofchampionhill.org/history/series4.htm

The post script notes the house was moved to a location close to the Confederate Cemetery in Raymond in 2006. Interestingly it was sold in 2019 and you can see pictures on Zillo. Much confusion reigns as the RCC has 140 confederate dead buried from the Battle of Raymond which occurred in April, 1863 before Grant turned towards Jackson. Hiawatha Plantation was involved in Baker's Creek or
Champion Hill May 16, 1863. As the history article reports the house was across the road from where Gen. Tilghman was killed which is marked with a Stone Monument. This is on "Cotton Hill" east of Baker's Creek on the Raymond - Baker Road.

https://www.nps.gov/vick/learn/historyculture/tilghmanmon.htm

This list is the best I've found of dead from the battle and refers back to the Bakers Creek Burial ground.

http://battleofchampionhill.org/killed.htm

I suspect that most if not all ended up in those burial trenches. This part of Mississippi is pretty in tune to taking care of their "boys" even today and if not buried there then other burial locations would be known. For example the 2 soldiers in RCC.