I can change the alignment of dynamics relative to noteheads. Is there a way to do a similar thing to playing techniques (except for moving the text manually)?
No, glyph-based playing techniques are always centred on the notehead, while textual ones are left-aligned. You could try creating a glyph-based one and adding text as the contents of the symbol. We may at some point in the future add a property for this, but it’s not something we’re actively working on at the moment.