Not sure what your current code looks like, but you can try this. It will change the orientation of your vertical linear dimensions. (Reference link) Or do you want it to still be 'Parallel' & displayed above the line as shown in your pictures?
Dim oDoc As DrawingDocument = ThisApplication.ActiveDocument
Dim oDimStyle As DimensionStyle
oDimStyle = oDoc.StylesManager.DimensionStyles.Item("YourStyle")
oDimStyle.VerticalDimensionTextOrientation = kInlineAlignedDimensionText
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