I think the cursive Ped. is a product of the nineteenth century and shouldn’t be used in modern scores. Because it is a technique, it should be lower case in plain text. (I also think l.h. and r.h. should be lower case too for the same reason.) I don’t use the horizontal line because it clutters up the score. I am unable to figure out how to make the pedaling technique in the program to display this way. I put in my preferred pedal markings in the score below, but they print about a centimeter lower than they display on the screen. The font is Bravura Text. What’s going on?
Can you supply a sample document, with all your customizations, that exhibits the problem? Are you using Playing Techniques, or Text objects for the marks?
Wait till I tell you how old the clefs are! 
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Lombardi.glass.2.dorico (1.4 MB)
They are text objects. I wish there was an expressions objects separate from text objects.
The text objects do not seem to be in the file you have sent. (Though they are in the QuickLook file preview.)
I see that you have added the real Pedal lines and hidden them by making them 0% Opacity.
I suspect that the text objects are trying to avoid the Pedal lines. Try unchecking the Property for the Text objects to avoid collisions in Engrave mode.
PS: I suspect the punctuation after “girl” should be a comma?
I delayed in responding because there’s another issue. My Dorico 6 trial expired the day I posted my file. All the pedaling text objects are gone in Dorico 5. My department purchased the upgrade to Dorico 6 about two months ago, and we’re still waiting on Steinberg.
I already had the avoid collisions property unchecked. Right before my trial expired, I learned that exporting to pdf keeps the pedaling in the right place.
The punctuation on the poem is correct. If you saw the whole poem, you would see why.