Yes, you can use terminal or Synaptic. Synaptic relies on your sources list in the same manner as APT does.
Zorin OS comes with all the Zorin Repos added. So, either installation method will see them.
That aside, I have no idea of the cause.
Until your thread, I was examining exclusively code in Gnome-Shell (With no results as of yet) wondering of that was where the fault is.
I believe tan10vir is also using Core (Gnome).
So either coincidence or something outside of gnome or XFCE is affecting panels on both...
Another post:
For XFCE users that experience panel issues on login or unlock, you might avoid having to restart by hitting alt+F2 and entering in "xfce4-panel --restart" without quotes.
Gnome users may be able to with alt+F2 and entering in "r" without quotes to restart the gnome-shell.