Have you tried running FTL in a windowed mode, and looking at all the options KDE offers for managing windows? You can click the icon at the top-left of the window, you should get a KDE menu with many options. Maybe there is a way to tell KDE to keep the window on a particular screen? I cannot check on this computer unfortunately, and I don't have a dual-screen setup, so I don't know much about that.
I also run Kubuntu, with a 1280x720 screen. I'm lucky, that's the size of the FTL window.

I use the KDE options to remove the windows borders altogether, this gives me the best of both world: the game covers the whole screen, and I can very smoothly Alt-Tab to other applications.
If you cannot find a way to pin the FTL window to a particular screen, maybe you can try to set that screen to 1280x720, put the FTL window there, and finally remove the window borders.
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