So looking at that article it seems most of the casualties were after the Wilderness. At the bottom it reads:
"The majority of these casualties were sustained June 1st, in driving the enemy's skirmishers and sharpshooters from their position behind the timer(?), while our line was exposed to a gatling (?) fir as it advanced across an open plain."
Some of the individual records soldier mentions are noted to be different in parenthesis, such as "(done in the Wilderness, but not then reported)".
That would place his death likely on June 1st which is the Battle of Cold Harbor. Looking at books (with google search, though I don't own them so getting only snippets) it seems Anderson's brigade was involved in some efforts on June 1st so seems to match up.