For gtk, gstreamer etc. PyGObject should just work. It has PyPy as part of its CI pipeline. Also in combination with matplotlib (GTK3Cairo backend) and numpy.
Thanks, but I mentioned I don't want to use Gtk. I've not had a particularly joyous time with Gtk in the past and therefore chose Qt as my GUI platform of choice over Gtk.
Therefore until and unless PyPy has usable Qt bindings (e.g. PySide or PyQt), then unfortunately I need to stick with CPython :/
Not sure about PySide2..