I see what happened. Those Dimensions have the underlining done by adding %%U before and after the < or > character, as it's done in plain Text. Dimension text is "Mtext-like" in certain ways, including in the editing options in the ribbon. If I have a Dimension with < or > added as part of a text override, and if I select that character in editing the Dimension text and choose the Underline icon in the ribbon:

it does the underlining with the Mtext approach:
"{\\L<}<>"
The routine expects the %%U approach only in plain Text, so for other object types it looks only for the {\\L approach. So it works when the underlining is done by the icon in the ribbon [like editing Mtext], but not when it's done with %%U wrappers.
The oddest thing about it, to me, is that when editing Dimension text, you get the same editing ribbon as you do for Mtext, so I expect it to be the same, but it's not quite. For some reason the %%U wrappers work to underline things in Dimension text, though they do not work in Mtext. In Dimension text, for some reason you can underline in two ways, but in Text or Mtext, only one each. I wasn't aware of that duality in Dimension text when I wrote the routine.
SO I took out the limitation of what it looks for by entity type, and the attached now looks for any of those ways of underlining, in any kind of object. It works in your drawing, in quickie testing.
Kent Cooper, AIA