I was able to get it to work with this. Unfortunately, My tables are still rolling over pages, but that's another problem.
Code:
For Y = 0 To LargeTable.Rows.Count
X = 0
Do While X < LargeTable.Columns.Count
If LargeTable.Cell(Y, X).Tables.Count = 1 Then
X = X + 1
LargeTable.Rows(Y - 2).Select
Selection.ParagraphFormat.KeepWithNext = False
Exit Do
End If
X = X + 1
Loop
Next Y