Belated thanks to Adriano for linking me through to that post.
Just to say, what I was looking for was actually incredibly simple.
Rather than copying the CSS, HTML or glyph, you just need to add the textual version of the dashicon i.e ‘dashicons-menu’ or ‘dashicons-dashboard’ to the ‘Menu Icon’ field under the ‘Visibility’ box in your CPT settings.
Hope this helps!
