The Union generally counted the mortally wounded among the killed when they died relatively shortly after the battle, so the majority of the mortally wounded would already be counted (although there is still some wiggle room).
That's the thing, both my samples used Union data. Granted they're only cases for officers, but the entries in the returns still indicated more named total deaths (including KIA and MWIA) than the numerical KIA count.
In that case, Col. Trevor Dupuy's classic study shows that for the American Civil War, the ratio of killed to wounded was 4.55:1 and the ratio of surviving wounded to battle deaths was 2.38:1. You could try applying those ratios to come up with a reasonable estimate of the total number of deaths. Hope this helps.
I'm going to assume here that the Union and the Confederacy were roughly comparable in their KIA/WIA/MIA ratios and that the CSA had 3/5 of the casualties of the Union. It's imperfect but let's call it the 3/5 compromise.
Official Union figures based on their returns are:
7,621 KIA
38,339 WIA
Total KIA/WIA = 46,000
Expected killed to wounded ratio 4.55:1
Expected killed to wounded 37,711:8,288
Expected ratio of surviving wounded to battle deaths 2.38:1
Expected breakdown 32:390:13,609
This suggests to me that, if the Overland is statistically typical:
1) At least some of the MIA were actually killed, though not many.
2) The Union count of MWIA was on the order of 5,000.
This would give a figure for the whole campaign including the Confederates of:
KIA 13,280
MWIA 8,000
For a total death count in the vicinity of 21,000-22,000
This is a greater MWIA impact than what we'd expect from my (admittedly scant) hard data on officers - possibly officers got better medical care and were more likely to survive, or possibly the situation of the Overland was atypical and the statistical approach doesn't really apply here. I'd have expected it to if anything go the other way though, at least due to the trench warfare (which would bias KIA/WIA towards head wounds.)
I think the best estimate we can produce is that the KIA is 11,000-13,000, and that MWIA may increase this by as much as another 9,000 (though we can't be confident about more than a few thousand). This uncertainty is, unfortunately, pretty typical for the period.